prove that 1/2{SinA/1+cosA+ 1+cosA/sinA}= 1/SinA
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Solution :
On Solving LHS
➨ 1/2 { SinA/1 + cosA + 1 + cosA/sinA }
➨ 1/2 { [ sin² A + ( 1 + cos A )² ] / ( sin A ) ( 1 + cos A }
➨ 1/2 { [ sin² A + 1 + cos² A + 2 cos A ] / ( sin A ) ( 1 + cos A }
➨ 1/2 { [ 1 + 1 + 2cos A ] / ( sin A ) ( 1 + cos A ) }
➨ 1/2 { [ 2 + 2cos A ] / ( sin A ) ( 1 + cos A ) }
➨ 1/2 *2 { 1 + cos A } /( sin A ) ( 1 + cos A ) }
➨ 1 / sin A
Which is equal to LHS
Hence Proved
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