Question

Prove the following trigonometric identities. $\frac{1+sec\Theta}{sec\Theta}=\frac{sin^{2}\Theta }{1-cos\Theta}$

Answer 1

Answer with Step-by-step explanation:

Given :  

(1 + secθ) / secθ = sin²θ/(1− cosθ)

LHS :   (1 + secθ) / secθ

= (1 + 1/cosθ)/(1/cosθ)

[By using the identity, secθ = 1/ cosθ ]

= [(cosθ + 1 )/cosθ] × cosθ/1

[By taking LCM]

= 1 + cosθ

RHS = sin²θ/(1− cosθ)

= (1– cos²θ)/(1−cosθ)

= [(1−cosθ)(1 + cosθ)] /(1− cosθ)

[By using identity = a² - b² = (a + b) (a - b) ]

= 1 + cosθ

(1 + secθ) / secθ = sin²θ/(1− cosθ)

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

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