[I_(0)sin^(4)x+sin^(2)x=1],[" then prove that "tan^(4)x-tan^(2)x=1]

Prove that sin 2x=(2 tan x)/(1+tan^(2)x)

if m=tan x+sin x and n=tan x-sin x then prove that m^(2)-n^(2)=4sqrt(mn)

(i) 4cos^(2)x=1 (ii) 4sin^(2)x-3=0 (iii) tan^(2)x=1

If x_(1),x_(2),x_(3),andx_(4) are the roots of the equations x^(4)-x^(3)sin2 beta+x^(2)cos2 beta-x cos beta-sin beta=0, prove that tan^(-1)x_(1)+tan^(-1)x_(2)+tan^(-1)x_(3)+tan^(-1)x_(4)=n pi+((pi)/(2))-beta, where n is an integer.

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

If x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3)) , then prove that y^2 = 1 - x

If cos x + cos y =(1)/(3) and sin x + sin y=(1)/(4) prove that tan ((x+y)/(2))=(3)/(4)

" If "I=int(cos^(3)xdx)/((sin^(4)x+3sin^(2)x+1)tan^(-1)(sin x+cos ecx)),=-A log|tan^(-1)(sin x+cos ecx)|+C" ,then A is equal "