Question

01.(I + Cosecθ) (1 - Sinθ ) = ?
(a) Sinθ.Cosθ
(b) tanθ.cotθ
(c) Cosθ.cotθ
(d) cosecθ.cotθ​

Answer 1

Step-by-step explanation:

$(1 + \cosec(a))(1 - \sin(a) )$

$= (1 + \frac{1}{ \sin(a) } )(1 - \sin(a)$

$= ( \frac{ \sin(a) + 1}{ \sin(a) } )(1 - \sin(a) )$

$= (1 - { \sin }^{2} a) \div \sin(a)$

$= \frac{ { \cos }^{2}a }{ \sin(a) } = \cos(a) \times \frac{ \cos(a) }{ \sin(a) }$

$= \cos(a) \cot(a)$