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Question
Prove the following:
`(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` = secθ
Solution
L.H.S. = `(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))`
= `(sin(theta/2)/(cos(theta/2)) + cos(theta/2)/sin(theta/2))/(cos(theta/2)/(sin(theta/2)) - sin(theta/2)/(cos(theta/2))`
= `(sin^2(theta/2) + cos^2(theta/2))/(cos^2(theta/2) - sin^2(theta/2)`
= `1/costheta`
= sec θ
= R.H.S.
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