Question

sin A/1+cos A= cosec A - cot A​

Answer 1

Answer:

sinA/1+cosA=cosecA-cotA

sinA/1+cosA=1/sinA-cosA/sinA

sinA/1+cosA=1-cosA/sinA

sin^2 A=1-cos^2 A(by cross multiplying)

sin^2 A=sin^2 A

1=1

Step-by-step explanation:

hence proved LHS=RHS

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Answer 2

$\:\:\:\: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \huge\mathcal{\bf{\underline{\underline{\huge\mathcal{Answer}}}}}$

$\large\mathcal\red{solution}$

$l.h.s. = \frac{ \sin(a) }{1 + \cos(a) } \\ = \frac{2 \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) }{2 \cos {}^{2} ( \frac{a}{2} ) } \\ = \frac{ \sin( \frac{a}{2} ) }{ \cos( \frac{a}{2} ) } \\ = \tan( \frac{a}{2} ) \\ r.h.s. = \cosec(a) - \cot(a) \\ = \frac{1}{ \sin(a) } - \frac{ \cos(a) }{ \sin(a) } \\ = \frac{1 - \cos(a) }{ \sin(a) } \\ = \frac{2 \sin {}^{2} ( \frac{a}{2} ) }{2 \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) } \\ = \frac{ \sin( \frac{a}{2} ) }{ \cos( \frac{a}{2} ) } \\ = \tan( \frac{a}{2} ) \\ therefore \: \: l.h.s. = r.h.s.(proved)$

$\large\mathcal\red{hope\: this \: helps \:you......}$