Question

please solve this question

Answer 1

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Answer 2

Take theta as x .

L.H.S

( sec x - 1 ) / ( sec x + 1 )

⇒ ( 1/cos x - 1 ) / ( 1/cos x + 1 )

⇒ ( 1 - cos x ) / cos x / ( 1 + cos x ) /cos x

⇒ ( 1 - cos x ) / ( 1 + cos x )

Now we need to multiply and rationalise the denominator :

⇒ ( 1 - cos x ) / ( 1 + cos x ) × 1

⇒ ( 1 - cos x ) / ( 1 + cos x ) × ( 1 + cos x ) / ( 1 + cos x )

⇒ ( 1 - cos²x ) / ( 1 + cos x )²

⇒ sin²x / ( 1 + cos x )²

⇒ ( sin x / 1 + cos x )²

Hence proved !