If `sintheta=1/2(x+1/x)`, show that `sin3theta+1/2(x^3+1/x^3)=0`

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

If cos2theta=x+1/x , prove that 2cos3theta=x^3+1/x^3

If tan theta+sec theta=x" show that 2 tan "theta=x -1/x, 2 sec theta=x+1/x. Hence show that sin theta=(x^(2)-1)/(x^(2)+1)

If (x+1/(x))^(2)=3 , show that x^(3)+1/(x^(3))=0

If 2 cos theta = x + (1)/(x), prove that 2 cos 3 theta = x ^(3) + (1)/(x ^(3)).

tan theta+sec theta=x show that 2tan theta=x-(1)/(x),2sec theta=x+(1)/(x) hence prove that sin theta=(x^(2)-1)/(x^(2)+1)

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

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