If `costheta= 1/2(a+1/a),` show that `cos2theta = 1/2*(a^2 + 1/(a^2))`

If costheta=1/2(a+1/a), show that : cos3theta=1/2(a^3+1/a^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))

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 costheta=tan^2((theta)/2) show that costheta=sqrt2-1

IF 2 costheta=x+1/x then show that 2 cos3 theta=x^3+1/x^3

If costheta=a then show that cos^(2)((theta)/(2)) and sin^(2)((theta)/(2)) are roots of the equation 4x^(2)-4x+1=a^(2) .

If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos2^(2) theta cos2^(3) theta.... cos2^(n-1) theta = 1.

If 2costheta=x+1/x , then 2cos2theta= ?

If 2costheta=x+1/x , then 2cos2theta= ?

If costheta+cos^2theta=1 ,show that 1/(cosec^2theta)+1/(cosec^4theta)=1