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1. Prove the following trig identity
tan(x/2)=sinx/1+cosx​

User Gbixahue
by
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1 Answer

4 votes

Explanation:


\tan( (x)/(2) ) = ( \sin(x) )/(1 + \cos(x) )


\tan( (x)/(2) ) = ( √(1 - \cos(x) ) )/( √(1 + \cos(x) ) )

So we have


( √(1 - \cos(x) ) )/( √(1 + \cos(x) ) ) = ( \sin(x) )/( √(1 + \cos(x) ) )

Next, we then rationalize the numerator so we get


( √(1 - \cos(x) ) )/( √(1 + \cos(x) ) ) ( √(1 + \cos(x) ) )/(1 + \cos(x) ) = \frac{ \sin(x) }{ {1 + \cos(x) } }

The denominator should be square root so to let you know .

So know we ahev


\frac{ \sqrt{1 - \cos {}^(2) (x) } }{1 + \cos(x) } = ( \sin(x) )/(1 + \cos(x) )


\frac{ \sqrt{ \sin {}^(2) (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } }


( \sin(x) )/(1 + \cos(x) ) = ( \sin(x) ) )/(1 + \cos(x) )

User Rec
by
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