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prove that: cos 2 theta÷1-tan theta+sin 2 theta÷1-cot theta = 1+sin theta×cos theta

prove that:
cos2theta÷1-tan theta+sin2theta÷1-cot theta = 1+sin theta×cos theta

Grade:10

1 Answers

Vikas TU
14149 Points
5 years ago
Taking L.H.S
cos2theta/(1-tan theta)  +  sin2theta/(1-cot theta)
change tanthetha and cotthetha into sin and cos.
 => cos^thetha/(costhetha – sinthetha) – sin^3thetha/(sinthetha -costhetha)
=> (cos^3thetha – sin^3thetha)/(costhetha -sinthetha)
=> (costhetha-sinthetha)(1 + sinthethacosthetha)/ (costhetha-sinthetha)
=>  1+sin theta×cos theta
Helce proved.

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