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prove that (cosecθ+cotθ-1)/(cotθ-cosecθ+1)= sinθ/1-cosθ

prove that (cosecθ+cotθ-1)/(cotθ-cosecθ+1)= sinθ/1-cosθ

Grade:10

1 Answers

Rajat
213 Points
5 years ago
(cosec X + cot X -1)/(cot x - cosec X + 1)
we know that, cosec^2x-cot^2x=1
So, LHS=  (cosec X + cot x +cot^2x -cosec^2x)/(cot x -cosec X + 1)
= [(cotx+cosecx)+(cotx+cosecx)(cotx-cosecx)]/(cotx-cosecx+1)
=(cotx+cosecx)(cotx-cosecx+1)/(cotx-cosecx+1)
=(cotx+cosecx)= (cosx+1)/sinx=sinx(cosx+1)/sin^2x
=sinx(cosx+1)/(1-cos^2x)
=Sinx/1-cosx 
 
Done!

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