Question

1+cos-sin^2/sin(1+cos) =cot​

Answer 1

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

Solution :

LHS =

$= \frac{1 + cos \: - {sin}^{2} }{sin(1 + cos)} \\ \\ = \frac{ ({sin}^{2} + {cos}^{2}) + cos - {sin}^{2} }{sin(1 + cos)} \\ \\ sin \: \: gets \: \: cancelled \: \: bcz \: \: different \: \: sign \\ \\ = \frac{ {cos \: + cos}^{2} }{sin(1 + cos)} \\ \\ take \: \: out \: \: the \: common \: term \: \\ in \: numerator \: \: \: \: i.e. \: \: \: \: cos \\ \\ = \frac{cos(1 + cos)}{sin(1 + cos)} \\ \\ (1 + cos \: ) \: \: \: gets \: cancelled \\ \\ = \frac{cos}{sin} \\ \\ = cot$

= RHS

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Answer 2

$\frac{1 + cos - {sin}^{2} }{sin(1 + cos)} \\ \\ = \frac{ {cos}^{2} + cos}{sin(1 + cos)} \\ \\ = \frac{cos(cos + 1)}{sin(1 + cos)} \\ \\ = \frac{cos}{sin} \\ \\ = cot$