Question

Prove the following trigonometric identities. $\frac{1-cos\Theta}{sin\Theta}=\frac{sin\Theta}{1+cos\Theta}$

Answer 1

Answer with Step-by-step explanation:

Given : (1−cosθ) / sinθ = sin θ /(1+cosθ )

L.H.S : (1− cosθ)/ sinθ

Multiplying both numerator and denominator by (1+ cosθ),

= [(1−cosθ) (1 + cosθ)] / [(1 + cosθ) sinθ]

= (1− cos²θ)/ [(1+ cosθ)(sinθ)]

= (sin²θ)/ [(1+ cosθ)(sinθ)]

[By using the identity , 1 − cos²θ = sin² θ ]

= (sinθ)(1 + cosθ)

1 − cosθ/ sinθ = sin θ / (1 + cosθ)

L.H.S = R.H.S  

Hence Proved..

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Answer 2

$\huge\bf{Hey\:Mate}$

Refer to the attatchment!

Hops it helps uh✌️