Question

Prove 1+ sinx - cosx / 1+ sinx - cosx = tanx/2

Answer 1

Answer:

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Step-by-step explanation:

L H S

= 1 + sin x − cos x 1 + cos x + sin x

= sin x ( 1 + sin x − cos x ) sin x ( 1 + cos x ) + sin 2 x

= sin x ( 1 + sin x − cos x ) sin x ( 1 + cos x ) + ( 1 − cos 2 x )

= sin x ( 1 + sin x − cos x ) ( 1 + cos x ) ( sin x + 1 − cos x )

= sin x 1 + cos x

= 2 sin ( x 2 ) cos ( x 2 ) 2 cos 2 ( x 2 )

= sin ( x 2 ) cos ( x 2 )  = tan ( x 2 )

L H S

= 1 + sin x − cos x 1 + cos x + sin x

= sin x ( 1 + sin x − cos x ) sin x ( 1 + cos x ) + sin 2 x

= sin x ( 1 + sin x − cos x ) sin x ( 1 + cos x ) + ( 1 − cos 2 x )

= sin x ( 1 + sin x − cos x ) ( 1 + cos x ) ( sin x + 1 − cos x )

= sin x 1 + cos x

= 2 sin ( x 2 ) cos ( x 2 ) 2 cos 2 ( x 2 )

= sin ( x2 ) cos ( x 2 )

= tan ( x 2 )