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Q. The function f:R¬R is defined by, f(x) = cos?x + sin4x for x e R, then the, domain and range of f(x) is, 3, A, 4, B, 4, (;+), D, 2., cos? æ + sin' x, y = f(x), = y = f (x), %3D, cos? x + sin? æ (1 – cos² æ), > y = cos² x + sin? x –, sin?, x cos? x, = y = 1- sin? x cos? x, = y = 1 – sin? 2x, ..< f (x) < 1, + f (x) € [,1], %3D, -, (: 0 < sin? 2x < 1), RE, Find the domain and range of, 1, f (x) =, 3., %3D, 2 cos x, 1, W Edit with WPS Office

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-1 < cos a < 1, = -2 < 2 cos x < 2, = -3 < 2 cos x – 1<1, 1, For, 2 cos z-1, ,-3 < 2 cos x – 1<0 or 0 < 2 cos x – 1<1, <글 or1<, is (-∞, –] U [1, 0), 1, > -00 <, < 00, 2 cos z-1, 2 cos a-1, Hence, the, range, Find the domain and range of, f (x) =, 4., /log3 (cos (sin æ))., f (x) = Vlog3 (cos (sin a)), ||, f (x) is defined only if log3 (cos (sin x)) > 0, + cos (sin a) >1, + cos (sin æ) =1 as -1 < cos0 < 1, + sinx=0 = x=nT,n E I, Hence, the domain consists of the multiples of 7,i.e.,, Domain = {nn, n E I}, Also, the range is {0}., EDLCARE, Find the value of tan 15º, 5., W Edit with WPS Office

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cos0 – sin 0, LHS=, cos0 + sin 0, cos 0, sin 0, cos0, sin 0, +, cose, cos0, cos0, cos0, 1- tan 0, 1+ tan 0, tan, tan 0, 4, tan 0, 4, 1+tan, = tan, 4, RHS, tan x+ tan y_ sin(x+y), tan x– tan y sin (x- y)", Prove that, 7., tan x+ tan y, LHS =, tan x, - tan y, sin x, +, sin y, cos x, sin x, cos y, sin y, ARE, cos x, cos y, W Edit with WPS Office