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)

If cos theta=(1)/(2)(a+(1)/(a)), show that cos2 theta=(1)/(2)*(a^(2)+(1)/(a^(2)))

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 cos theta=(1)/(2)(a+(1)/(a)) then show that cos3 theta=(1)/(2)(a^(3)+(1)/(a^(3)))

If cot theta=(1)/(sqrt(3)), show that (1-cos^(2)theta)/(2-sin^(2)theta)=(3)/(5)

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

If "cosec"theta=2 , show that (cottheta+(sintheta)/(1+costheta))=2 .

If theta =(pi)/(2 ^(n) +1), then cos theta cos 2 theta cos 2^(2) theta …cos 2 ^(n-1)theta is equal to

If sintheta+costheta=x , then show that: sin^(6)theta+cos^(6)theta=1-3/4(x^(2)-1)^(2)