Question

sin A/1+cos A=sec A -cot A​

Answer 1

$\huge{\underline{\underline{\red{♡Solution→}}}}$

$\frac{sin \: a}{1 + cos \: a} =cosec \: a - cot \: a$

$\bold{\huge{\underline{\underline{\rm{ LHS :}}}}}$

$= \frac{sin \: a}{1 + cos \: a}$

Divide and multiply by 1 - cos a

$= \frac{sin \: a}{1 + cos \: a} \times \frac{1 - cos \: a}{1 - cos \: a}$

$= \frac{sin \: a(1 - cos \: a)}{(1 - cos \: a)(1 + cos \: a)} \\ = \frac{sin \: a - sina \: cos \: a}{1 - {cos}^{2} a} \\ = \frac{sin \: a - sin \: a \: cos \: a}{ {sin}^{2}a } \\ = \frac{sin \: a}{ {sin}^{2}a } - \frac{sin \: a \: cos \: a}{ {sin}^{2} a} \\ = \frac{1}{sin \: a} - \frac{cos \: a}{sin \: a}$

$= cosec \: a - cot \: a$

$\bold{\huge{\underline{\underline{\rm{ RHS ↑}}}}}$

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