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प्रश्न
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
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उत्तर
LHS = `((sin^2 A + ( 1 + cos A)^2)/((1 + cos A)sin A))`
= `(sin^2 A + 1 + cos^2 A + 2 cos A)/((1 + cos A) sin A)`
= `(1 + 1 + 2 cos A)/((1 + cos A) sin A)`
= `(2(1 + cos A))/((1 + cos A)sin A)`
= 2 cosec A
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
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[Hint : Simplify LHS and RHS separately.]
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`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
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`(tan A + tan B)/(cot A + cot B) = tan A tan B`
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