Question

Prove that sinx/1+cosx = tanx/2​

Answer 1

Answer:

Here's your answer

$\frac{ \sin(x) }{1 + \cos(x) } = \tan( {x}^{2} ) \\ \\ lhs \\ \\ rationalising \ \\ \frac{ \sin(x) }{1 + \cos(x) } \times \frac{1 - \cos(x) }{1 - \cos(x) } \\ = \frac{ \sin(x)(1 - \cos(x) )}{1 - \cos( {x}^{2} ) }$

Step-by-step explanation:

$= \frac{ \sin(x) (1 - \cos(x) }{ \sin( {x}^{2} ) } \\ \\ = \frac{1 - \cos(x) }{ \sin(x) } \\ \\ = \frac{1}{ \sin(x) } - \frac{ \cos(x) }{ \sin(x) } \\ \\ = \csc(x) - \tan(x)$

Answer 2

Answer:

We have

Sin x /1+Cos x=Tan x/2

Taking left hand side

=Sin x /1+Cos x

:- (Sin x = 2Sin x/2. Cos x/2)

And :-(1+Cos x= 2Cos ^2 x/2)

So,

2Sin x/2.Cos x/2

= - - - - - - - - - - - - - -

2Cos^2 x/2

Sin x/2

= - - - - - - - -

Cos x/2

= Tan x/2

Hence proved

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