1. cos 0 = 79 tan = 1 V2

2tan ^ (- 1) (cos x) = tan ^ (- 1) (2cos ecx)

Find the magnitude of angle A, if : (i) 2 cos^(2)A - 3 cos A + 1 = 0 (ii) 2 tan 3A cos 3A - tan 3A + 1 = 2 cos 3A

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ""(x)/(2) tan ""(y)/(2))

If x != 0 , then tan((pi)/4 + 1/2 cos^(-1) x) + tan ((pi)/4 - 1/2 cos^(-1) x) = ......

prove that tan ((pi) / (4) + (1) / (2) cos ^ (- 1) ((a) / (b))) + tan ((pi) / (4) - (1) / (2) cos ^ (- 1) ((a) / (b))) = (b) / (a) cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y) ) = 2tan ^ (- 1) ((tan x) / (2) (tan y) / (2))

y = tan ^ (- 1) ((1) / (cos ^ (2) x + cos x + 1)) + tan ^ (- 1) ((1) / (cos ^ (2) x + 3cos x + 3)) upto n terms then y '(0) =

Prove that : (tan A + (1)/ (cos A))^(2) + (tan A - (1)/ (cos A))^(2) = 2 ((1 + sin^(2) A)/ (1 - sin^(2) A))

If alpha, beta are roots of the equation (1 + cos theta) tan^(2) x - lambda tan x = 1 - cos theta where theta in (0, (pi)/(2)) and cos^(2) (alpha + beta) = (1)/(51) then lambda is :

The number of solutions of the equation cos 6 x + tan^(2) x + cos 6 x tan ^(2) x = 1 , in the interval [0, 2 pi] is