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JEE - Inverse Trigonometric Functions, PH-8980322383/9898553283(SHAILESH SIR ), -1, x) =, РЕT 1988; MNR, (b), 9., cos(tan, [MP, (a), 1981], 1, (a) Vi+x?, (b), (c), (d) None of these, +x, 19., The value of sin cot tan cos, x is equal to, (c) 1+x?, (d) None of these, [Bihar CEE 1974], 10., tan sec, +x, (а) х, (b), (a)는, (b) x, (c) 1, (d) None of these, 1, sin, -1, is equal to, 20., (c), Vi+x?, (d), V1 + x, Vx + a, sec " [sec(-30°)] =, [MP PET 1992], (a) cos, --, 11., (b) cosec, (а) — 60°, (b) – 30°, (c) 30°, (d) 150°, (c) tan, (d) None of these, a, cos x, 12., tan, 1, + cosx, 5, 1+ sin x, If sin sin, 1, then x is equal to, 21., (a), 4, (b), 2, [MNR 1994; Kerala (Engg.) 2005], (а) 1, (b) o, (c) 2, (d) -x, 1, (c), (d) -, 1, --, 13., tan, 2, 1, 22., If sin x = 0 + B and sin, y = 0 - B, then 1+ xy =, (a) sin? 0 + sin? B, (b) sin? 0 + cos ? B, (a) 2, (b), + cosec, + sec, (c) cos? 0 + cos? B, (d) cos? 0 + sin? B, (c) cosecx, (d) sec-x, 2, = sin, -1, 23., If sin, + sin, x, then x is equal to, 14., The principal value of sin, is, [Roorkee 1995], (a) 3, V5 -4/2, (b), (b), (a) o, 9, V5 + 42, (c) -3, (d), (c), (d), 9, 15., sec (tan 2)+ cosec 2(cot 3) =, [ЕАМСЕТ 20o1], OR, 24., tan(cos, x) is equal to, [IIT 1993], (b) 13, (а) 5, (c) 15, - x, (b), 1 + x², (d) 6, (a), 16., sin-, x/1 -x - x V1 -x?, =, (c), (d) v1 –x?, (a) sinx + sin Vx, (b) sinx – sin Vx, 1-, 25., The domain of sin x is, [Roorkee 1993], (c) sin Vx – sinx, (d) None of these, (a) (-7, 7), (b) [-1, 1], 1, -1, tan, -1, 1-x, 17., If tan, x, then x =, (с) (0,2л), (d) (-0, 0), %3D, 1+x, 2, (a) 1, (b) V3, The principal value of sin-, is, 2, 26., [Roorkee, (c), (d) None of these, 1992], -27, (a), (b) *, 18., cos, cos, SHRE

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JEE - Inverse Trigonometric Functions, PH-8980322383/9898553283(SHAILESH SIR ), 36., sec(cosec x) is equal to, [Kurukshetra, CEE, (c), 3, (d), 3, 2001], 7, (a) cosec (sec x), (b) cot x, 27., cot cos, [Karnataka CET 1994], 25, (с) л, (d) None of these, 37., The range of tan x is, [DCE 2002], 25, (a), 24, 25, (b), 7, (), (а) л., (b), 2 2, 24, (c), 25, (d) None of these, (с) (-л, л), (d) (0, л), 38., 0 = sin [sin(-600°)], then one, the possible, then sin (sin x) is equal to, 2, 28., If, value of 0 is, (а) х, (с) л +х, (b) -x, (d) n - x, [Kerala (Engg.) 2002], GUR, (a) -, (b), 29., If 7<x < 27 , then cos(cos x) is equal to, -27, (а) х, (b) -х, (c), (d), 3, (с) 2л +х, (d) 2л — х, The value of sin(sin 10) is, The solution set of the equation sinx = 2 tan -, 39., is, 30., (a) 10, (b) 10-3л, [AMU 2002], (с) Зл -10, The smallest and the largest values of, (d) None of these, (а) {1, 2}, (c) {-1,1, 0}, 40. The value of cos(tan(tan 2)) is, (b) {-1, 2}, (а) {1, 1/2, о}, 31., tan, 0 <x<1 are, 1+ x, [AMU 2002], (b) 0,, 4, 1, (b), (а) 0, л, (а), (c) cos 2, (d) - cos 2, (c), (a), 4'4, If sin, x + sin y + sin z =, then the value of, 2, 32., If x takes non-positive permissible value, then, 41., sin, x?, v² +z +2xyz, equal to, (b) 1, (d) 3, [Pb. CET 2002], -1, (а) сos, (b) - cos v1 - x?, (a) o, (с) 2, - x, -1, (с) cos, (d) 7- cos V1 – x?, Vx, 1, V3, sin-, -1, 42., sin, sin tan, 4, [ЕAMСЕТ 1983], 33., (b), V3, (a), (b), 2, (a), 9, (c), 25, (d), 2, (d), (c), 57, 43. sin[cot (cos tan x)]=, 34. The principal value of sin, sin, is [MP, PET, 3, (a), (b), 1996], x'+2, + 1, 5л, (a), 3, 5л, (b), 3, 1, +1, (c), (d), x + 2, .2, 2, (c), (d), 3, 44., If sin(cot(x + 1) = cos(tan x), then x =, 35. The value of x which satisfies the equation, [IIT Screening 2004], 1, (a) -2, tan-x = sin-!, is, [Pb. СЕТ 19991, (b), V10, (a) 3, (b) -3, (с) о, (d), 1, (с), 3, 1, (d), 3, ON KIN

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JEE - Inverse Trigonometric Functions, PH-8980322383/9898553283(SHAILESH SIR ), 4, (a) x +y +z - xyz = 0, (b) x +y +z + xyz = 0, -1, 45., cos, + tan, 5, 5, (c) xy + yz + zx +1 = 0, (d) xy + yz + zx -1 = 0, 27, 11, (b) sin-, 27, -1, x - 1, (a) tan, 11, -1, If tan, 55., + tan - X +1, then x =, x + 2, x + 2, 4, 11, (c) cos, 27, -1, (d) None of these, 1, (a), 1, (b), /2, 1, + cos, 1, x + cos, -1, 46., sin, x + sin, (с) +, (d) +, (а) л, (b) 2, 1-, 56., cos V1 - x + sin, 1-x =, (с), 2, (d) None of these, (b) -, (а) л, GU, 1, 2 tan -, + tan, 3, (с) 1, (d) o, 47., (а) 90°, (c) 45°, 1, + sin -, 5, (b) 60°, 57., cos 2 cos, [IIT 1981], (d) tan 2, 2/6, (a), 5, 216, (b), 48., tan 90° - cot -, 5, (c), (d) -3, (а) 3, (b), 1, (c), a - b, b-c, -1, tan, (d), V10, 58., + tan, 1+ ab, 1+ bc, -1, a - tan - b, 4, + tan, 5, (a) tan, (b) tan -, a - tan c, 49., tan cos, (c) tan-b – tan -, (d) tan c– tan, -1, a, [IIT 1983; EAMCET 1988; MP PET 1990; MNR 1992], -1, 59. If tan, 2x + tan, 3x =, then x =, (а) 6/17, (b) 17/6, (d) 16/7, 4., (c) 7/16, [Roorkee 1978, 80; MNR 1986; Pb. CET 2001;, 50., tan 1+ tan, 2+ tan 3 =, Karnataka CET 2002], (b) -, 1, (b), 6., (a), (а) - 1, 4, (0) -1., (с) о, (d) None of these, (d) None of these, 5, I-, cot, + sin, 4, 51., 13, 60. If cot, x + tan, , then x =, 63, (a) sin, 65, 12, (b) sin, 13, 1-, (a) 1/3, (b) 1/4, FOR, (d) 4, 5, (d) sin, 12, -| 65, 1-, (c) sin, 68, 24, +cos -I, 25, 61., 2 sin, 5, 52., If cosx + cos, -1, y + cos, z = T, then, [Roorkee 1994], (a) x? +y? + z?, (b), 3, (a), 0 = záx +, (b) x? +y? +z? + 2xyz = 0, 57, (c), 3, (d) None of these, (c) x? +y? +z + xyz = 1, (d) x? +y? +z? + 2.xyz = 1, 1, + tan, 62., cos tan, 53., If tan-x - tan, -1, y = tan, A, then A =, [MP РЕT 1988], (а) х —у, (b) x +y, [MP PET 1991; MNR 199o], x +y, 1, (a), X -y, (b), (c), 1+ xy, (d), 1- ху, If tan x + tan, -1, y + tan, then, 2, (c), (d) *, 54., [Karnataka CET 1996]

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JEE - Inverse Trigonometric Functions, PH-8980322383/9898553283(SHAILESH SIR ), 63., tan, x + cot, (X +1) =, 2a, 26, -1, -1, 73., If sin, + sin, = 2 tan, x, then x =, -1, 1+a, 1+b?, -1, (a) tan, (x +1), (b) tan(x, 2, +x), [MNR 1984; UPSEAT 1999; Pb. CET 2004], (c) tan(x + 1), (d) tan(x, 2, +x +1), a -b, (a), 1+ ab, b, (b), 1+ ab, yz +1, zx +1, 64., cot, + cot, + cot, z - x, b, (c), 1- ab, X-y, y -z, a +b, (d), 1- ab, (а) о, (b) 1, 1, (c) cot, 1, is equal to, 2, x + coty + cotz (d) None of these, -+2 sin, 2, 74., cos, 65. If tan - a+x, a, -1 a-x, + tan, ,then x =, 6, [MP PET 1998; UPSEAT 2004], a, (a) 2/3a, (b) /За, (a), (b) 6, (c) 2/3a?, 2n, (d), 3, (d) None of these, (c), 4, = cos, 5, 1-, -1, 66. If cos, - sin, x. then x =, [AMU 1978], 3, tan, 5, 8, I-, 75., tan, tan, [AMU 1976, 77], 19, (а) о, (b) 1, (с) -1, (d) 2, (a), (b), 67., cot 3 + cosec, -15, (c), (d) None of these, (a) 3, (b), 1, - tan, 1, + tan, 70, 1, -1, 76., 4 tan, [Roorkee 1981], (c) T, 99, (d), (a), (b), 3, -1 1-x², tan, 1-x?, 1+x², 68., + cos, 2x, (c), (d) None of these, (a) -, (b), 2, 2л, then cos x + cosy =, 3, 4, 77., If sin x + siny =, (с) л, (d) o, [ЕАMСЕТ 1994], 69., If, tan (x – 1)+ tanx + tan (x + 1) = tan 3x ,then x, (a), (b) -, (a), (b) 0,, (c), (d) л, (с) 0,, 2, (d) 0,±-, 2, (), 78., tan, + tan, [ЕАМСЕТ 1994], 70., If cos, 1-, x + cos, y = 27, then sin, x + sin y is equal, OR, to, (a), (b) -sin, cos, (а) л, (b) -7, (c) 2, (d) None of these, (c), tan, (d) tan, 1, + cot, 3 is equal to, 71., sin-, X -), -1, - tan, is, x+y, 79., tan, [EAMCET 1992], [MP PET 1993; Karnataka CET 1995], (a) -, (b) 7, (a) *, (b), (c), (d) 2, Зл, (d) or, (c), 4, -1, x, then x =, -1, 72., If cot, a + cot, B = cot, [MP РЕT 1992], (a) a + B, (b) а - В, 80., If sin, -1, + cosec, then x =, 1+ ав, (c), a + B, aß – 1, (d), a + B, [ЕАМСЕТ 1983; Karnatakа СЕТ 2004]

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JEE - Inverse Trigonometric Functions, PH-8980322383/9898553283(SHAILESH SIR ), (а) 4, (b) 5, (a) k = 0, K = T, (b) k = 0, K =, %3D, (с) 1, (d) 3, (c) k =, (d) None of these, 81., 2 tan, 1-, + tan, [ЕАMСЕТ 19831, K = T, 57?, then x equals, 8, 49, 89. If (tanx)? + (cot x)² =, (a) tan, (b), 29, (а) -1, (b) 1, (с) о, (d) -, (с) о, (d) None of these, -1, 90. If tan(x +y) = 33 and x = tan, 3, then y will be, 15, + 2 tan, 17, 1-, 82., cos, [ЕAMCET 1981], (а) 0.3, (b) tan (1.3), URI, 1, (d) tan, 171, (а), 2, (c) tan (0.3), (b) cos, 221, 18, 23, then x =, 36, 2х -1, (c) A, 1-, = tan, (d) None of these, 91., If tan, + tan, x +1, 2x +1, [ISM Dhanbad 1973], 83., sin, + tan, 3 -3, (a), 4' 8, [Karnataka CET 1994], 3 3, (b), 4'8, (b), (а), 4, 4 3, (с), 3'8, (d) None of these, (с) cos, (d) a, -1 C,X - y, -1 C2 -C, + tan, 92., tan, Cy +x, 84. A, solution, of, the, equation, tan (1 + x), C3 - C2, 1+c3C2, 1, +... + tan -, tan, %3D, + tan (1 – x) =, is, [Karnataka CET 1993], (a, -1 y, tan, (b) tan yx, (а) х %3D1, (b) x = -1, (с) х%3D0, (d) x = t, (c) tan *, (d) tan(x - y), 85. If x? + y? +z? = r? , then, 1, + cos, 2, 93., sin{ sin, [ЕАМСЕТ 1985], -1 xy, tan, ZX, + tan, yr, -, tan, zr, (b) -1, (d) 1, (а) л, (b), 94., tan, [ISM Dhanbad 1971], (с) о, (d) None of these, 86., The, greatest, and, the, least, value, of, (b) 3, (sin x)' +(cos x)' are, (d) None of these, (a), (b), 2'2, x + cosx is equal to, 2002], 95., [Pb. CET 1997; DCE, (c), (d) None of these, 32, 1, then the number of solution of, 32, (a), 4, (b) 2, 87., If a<, (с) -1, (d) 1, (sin x) +(cosx) = an' is, 1, + tan, 2, -1, -1 1, 96., tan, (а) о, (b) 1, 3, (с) 2, (d) Infinite, [MP PET 1997, 2003; UPSEAT 2000;, 88. If k < sin x + cos, -1, x + tan x <K. then, -1, Karnataka CET 2001; Pb. CET 2004], (а) о, (b) л/4, GY, RE