sunb2 theta 1 0 cos2 theta 1 0 4 cos2 x 1 0 4 sin2 x

sunb^2 theta - 1 = 0 cos^2 theta - 1 = 0 4 cos^2 x - 1 = 0 4 sin^2 x - 3 = 0 9 tan^2 x - 3 = 0 3 tan^2 x - 9 = 0 sec^2 x - 2 = 0 4 sec^2 x - 2 = 0 (tan x - 1) (cos x + 1) = 0 (tan x + 1) (sin x - 1) = 0 (2 cos x + square root 3) (2 sin x + 1) = 0 (2 cos x - square root 3) (2 sin x - 1) = 0 cot x (tan x - 1) = 0 2 cos^2 x + sin x - 1 = 0 2 cos^2 - sin x - sin^2 x - 2 cos x - 2 = 0 4 sin^2 x + 4 cos x - 5 = 0 4 cos^2 x = 5 - 4 sin x 3 cos^2 x = sin^2 x sin 2 x = cos x sin 2x = sin x

Solution

54) Equate each factor to 0

tan x =-1 or sinx = 1

In the interval (0,2pi)

x = 3pi/4, 7pi/4, pi/2

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59) Take sinx as common factor

sin x(1+cosx) =0

Equate each factor to 0

x =0, pi, 2pi, pi

64) full question is not visible