Question

[sec A + tan A] [1 – sin A] =

Answer 1

Hope this answers the question

Answer 2

$\huge\mathcal\purple{\boxed{\boxed{Question}}}$

(sec A + tan A) (1 - sin A)

$\huge\mathcal\pink{\boxed{\boxed{Answer}}}$

$( \sec(A) + \tan(A) \: ) \: (1 - \sin(A)$

$= ( \frac{1}{ \cos(A) } + \frac{ \sin(A) }{ \cos(A) } ) \: (1 - \sin(A) \: )$

$= ( \frac{1 + \sin(A) }{ \cos(A) } ) \: \: (1 - \sin(A) \: )$

$= \frac{(1 + \sin(A) \: ) \: (1 - \sin(A) }{ \cos(A) }$

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

$= \frac{ { \cos }^{2}A}{ \cos(A) }$

$= \cos(A)$

So, (sec A + tan A) (1 - sin A) = cos A.

Hσρє ıт нєℓρѕ уσυ!