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(1+cot+tan)(sin-cos)

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(1+cot+tan)(sin-cos)

Posted by Jaya Singh 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

LHS = (1 + cot A + tan A)(sin A - cos A)
= sin A - cos A + cot A sin A - cot A cos A + tan A sin A - tan A cos A
=sin A - cos A + {tex}\frac{cos A}{sin A}{/tex} {tex}\times{/tex} sin A - cot A cos A + tan A sin A - {tex}\frac{sin A}{cos A}{/tex} {tex}\times{/tex} cos A
=sin A - cos A + cos A - cot A cos A + tan A sin A - sin A
=sin A tan A - cot A cos A
=RHS.

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