Question

Solve this trigonometrical question please​

Answer 1

Answer:

Answer is in the attachment

Answer 2

Answer:

Taking LHS from the question

Used formulas:

→ cos²θ = 1 - sin²θ

→ cosθ/sinθ = cotθ

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

using first formula

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

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

Using second formula

= cotθ

Concepts used:

→ trigonometric ratios

→ trigonometric identities