Question

Prove that sin theta/cot theta+cosec theta=2+sin theta/cot theta - cosec theta​

Answer 1

Answer:

L.H.S

Sinø /(1+cosø)

= Sinø (1-cosø) / (1+ cosø)(1-cosø)

[ multiply with (1-cosø) with denominator and numerator]

= (Sinø - Sinø . Cosø) / (1 - cos^2 ø)

= (Sinø - Sinø . Cosø) / sin^2 ø [ thus, Sin^2 ø + Cos^2 ø = 1 , so ,1- cos^2 ø = sin^2 ø ]

= Sinø/ Sin ^2 ø - Sinø. Cosø / sin^2 ø

= 1/ sinø - cosø / sinø

= Cosec ø - cot ø = R.H.S (proved)

Answer 2

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