Question

sin A÷
1 + cos A
= cosec A - cot A​

Answer 1

Answer:

hope it helps you friend.

Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer \: : }}}}}$

$\Large{\underline{\bf{To \: Prove \: :}}}$

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

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$\Large{\underline{\bf{Proof \: :}}}$

$\sf{ \leadsto \: \frac{sin \: a}{1 + cos \: a} = cosec \: a - cot \: a} \\ \\ \bf{Taking\:LHS }\\ \\ \bf{By \: rationalizing \: method} \\ \\ \sf{ \frac{sin \: a}{1 + cos \: a} \times \frac{1 - cos \: a}{1 - cos \: a} } \\ \\ { \boxed{ \orange{ \tt{(a + b)(a - b) = {a}^{2} - {b}^{2} }}}} \\ \\ \sf{\frac{sin \: a(1 - cos \: a)}{ {1}^{2} - {cos}^{2} a }} \\ \\ {\boxed{ \green{ \tt{1 - {cos}^{2}a = {sin}^{2}a }}}} \\ \\ \sf{ \frac{ \cancel{sin \: a}(1 - cos \: a)}{ { \cancel{sin}}^{2}a } } \\ \\ \sf{ \frac{1 - cos \: a}{sin \: a} } \\ \\ \sf{ \frac{1}{sin \: a} - \frac{cos \: a}{sin \: a} } \\ \\ \sf{cosec \: a \: - cot \: a} \\ \\ \huge{ \boxed{ \pink{ \mathcal{Hence \: Proved}}}}$

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