Question

sin theta by 1 + cos theta + 1 + cos theta by sin theta is equal to 2 cosecant theta​

Answer 1

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Answer 2

To prove that (sinθ/1+cosθ) + (1+cosθ/sinθ) = cosecθ

L.H.S:

(sinθ/1+cosθ) + (1+cosθ/sinθ)

By cross-multiplication,

sin²θ + (1 + cosθ)² / sinθ (1+cosθ)

Remember, sin²θ + cosθ² = 1

So when you expand,

(sin²θ + cos²θ + 1 + 2cosθ ) / sinθ (1 + cosθ)

2 + 2cosθ / sinθ ( 1+ cosθ)

2( 1 + cosθ) / sinθ ( 1 + cosθ)

2 / sin θ

2 (1/sinθ)  ⇒ 2 cosecθ

R.H.S

2 cosec θ

L.H.S = R.H.S, hence proved