Fill `1-.......=cos^2theta`

Fill in the blanks : 1 - ( --- ) = cos^2theta

Prove the following 1.((1-cos^(2)theta)/(sin^(2)theta))=12.1-((cos^(2)theta)/(1+sin theta))=sin theta

For all n in N, cos theta cos 2theta cos 4theta ....cos2^(n-1)theta equals to

1+cos theta=2cos^(2)theta

Prove that: (2cos2^(n)theta+1)/(2cos theta+1)=(2cos theta-1)(2cos2 theta-1)(2cos2^(2)theta-1)...(2cos2^(n-1)theta-1)

Prove that: (2cos2 theta+1)/(2cos theta+1)=(2cos theta-1)(2cos2 theta-1)(2cos2^(2)theta-1)...(2cos2^(n-1)theta-1)

cos theta+cos2 theta+cos3 theta+......+cos(n-1)theta+cos n theta=

For a positive integer n, let f_(n)(theta)=(2cos theta+1)(2cos theta-1)(2cos2 theta-1)(2cos(2^(2))theta-1)...(2cos(2^(n-1))theta-1) Which one of the following hold(s) good?

Prove that : sin^(4)theta + cos^(4)theta = 1 - 2 cos^(2) theta + 2 cos^(4)theta