How do you prove that $(sec^2theta)/2 = 2sin^2thetacsc^2(2theta)$ ?

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Answer 1 · 2015-12-13T21:34:02

Modify only the right side.

$2sin^2thetacsc^2(2theta)$

$=2sin^2theta(1/sin^2(2theta))$

$=(2sin^2theta)/(sin^2(2theta)$

Note that $sin(2theta)=2sinthetacostheta$ .

$=(2sin^2theta)/(2sinthetacostheta)^2$

$=(2sin^2theta)/(4sin^2thetacos^2theta)$

$=1/(2cos^2theta)$

$=sec^2theta/2$

How do you prove that (sec^2theta)/2 = 2sin^2thetacsc^2(2theta) (sec^2theta)/2 = 2sin^2thetacsc^2(2theta) ?