prove that (cosecθ+cotθ-1)/(cotθ-cosecθ+1)= sinθ/1-cosθ
prove that (cosecθ+cotθ-1)/(cotθ-cosecθ+1)= sinθ/1-cosθ
Ranjith Kanjoor , 7 Years ago
Grade 10
Trigonometry> prove that (cosecθ+cotθ-1)/(cotθ-cosecθ+1...
1 Answers
Rajat
(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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