Question

solve this question plz plz.............

Answer 1

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Answer 2

Answer :-


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To prove :-

√ ( 1 + sinA ) ( 1 - sinA ) = secA + tanA


Salutation :-

L.H.S = √ ( 1 + sinA ) ( 1 - sinA )

= √ ( 1 + sinA ) ( 1 - sinA ) × 1

= √ ( 1 + sinA ) ( 1 - sinA ) × √ ( 1 + sinA ) ( 1 + sinA )

[ • √ ( 1 + sinA ) ( 1 + sinA ) = 1 ]

= √ ( 1 + sinA ) ( 1 + sinA ) / ( 1 - sinA ) ( 1 + sinA )

= √ ( 1 + sinA )² / ( 1 )² - ( sinA )²

[ • Using identity - ( i ) ]

= √ ( 1 + sinA )² / ( 1 - sin²A )

= √ ( 1 + sinA )² / cos²A

[ • As we know , sin²∅ + cos²∅ = 1 , So , cos²∅ = 1 - sin²∅ ]

= ( 1 + sinA ) / cosA

= 1 / cosA + sinA / cosA

= secA + tanA

[ • We know , cos∅ = 1 / sec∅ and sin∅ / cos∅ = tan∅ ]

And R.H.S = secA + tanA

•°• L.H.S = R.H.S. [ • Hence Proved ]


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