Question

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Sinx/1+cosx +tanx/1+cosx = secx cscx -cotx


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Answer 1

Solution:-

Taking LHS

$\frac{ \sin(x) }{1 + \cos(x) } + \frac{ \tan(x) }{1 + \cos(x) } \\ \\ = \frac{ \sin(x) + \frac{ \sin(x) }{ \cos(x) } }{1 + \cos(x) } \\ \\ = \frac{ \sin(x)( 1 + \cos(x) )}{ \cos(x) (1 + \cos(x) )} \\ \\ = \tan(x)$

Now RHS

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

LHS = RHS

Hence, proved

Answer 2

Answer:

REFER TO ATTACHMENT FOR SOLUTION.

❣️ Regards KarnShubham ❣️