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Identities +, , , , , , , , , , A, I Base(B) B, , , , , , , , , , , , , , 2 2 AC’, S oo =sin’A + cos'A=1<—, rAB? AC? 2 !, nae ak =cot’Atl = cosec’A<BC = I, | |, Bc? _ ac? ap’ | | c !, ce = = I+tan’A=sec’A «4° C=, ag? AB? i QTE {, 3, 3 I, ZC, 2, 2, o, | oa |, |, |, |, |, |, J, , , , , , , , , , [oteasiansianiantenteniantaninetantentaetant a, , , , Complementary Ai, , , , , , , , , , , , , , , , , , , , , , , , , , , , AB AB _ AC, sin(90-A) = ae tan(90-A)= 5G cosec(90-A)= ae, AB AC, cosA = AG cota = = secA= 7, BC AC, cos(90-A)= 82 | cot(90-A)= qe | sec(90-A)= ge, , , , , , ~~, , bo _BC, sind = 5 tan =e, , , , eae, cosecA = BC, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , eee ewe eww eee wenn L, f e.g. If sin 30 = cos (0 - 6°) and ; re AB’ + BC’ =AC’ |, 30 and @ - 6° are acute, find the § ., ; volueof 0: ; ——-p} Trigonometric Ratios of Some Specific Angles, Sol. sin 30 = cos (@ - 6°) :, = cos (90° - 30)=cos(6-6°) 4, = 90°-30=0-6° ! 0° 30° 45° 60° 90°, = 40=96° T-ratios, = 0= 24°. ; 1 1 3, ' sin 0 = = 8 1, 4 e.g. If x=rsin® cos, y = r sind 2, 1 sino, z = r cos®, then Prove cos a 1 1 0, § that: x°+y?+2°=r’, 41 aoe a a, Sol. x = r sin® cos 1, y=rsind sino tan 0 acy 1 V3 Not defined, Z=r cosh 3, x+ryez 1, = u 8 cos’ 6+r’ sin’ 6 sin’ cot houcemes 3 1 V3 9, +r° cos’ 2, = r* sin’ @ (cos’ + sin’ 0) sec 1 = 2 2 Not define, +r° cos’ @ 3, =r’ sin’ 0+ r° cos’ 0 Zz, = (Gint 0 cos! 6) cosec | Not defined 2 Ae: 15 4, = Hl, , , , Simplified trigonometric values, , , , NCERT / X / Trigonometry