If `costheta= 1/2(a+1/a),` show that `cos2theta = 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 sintheta=1/2 , show that (3costheta - 4cos^3theta)=0

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

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

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

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

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

If sintheta+costheta=1 , then the value of sin2theta is

If costheta=(1)/(sqrt(2)) ,then find the value of cos2theta .

If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta) , then show that theta = (pi)/(4) , when n is an y integer.