Question

Please help me. Don't spam.
Solve this question. ​

Answer 1

Answer:

In the image.

Step-by-step explanation:

Hope this helps!

Answer 2

Required Answer:-

Given to prove:

$\rm \mapsto\dfrac{ \cos(x) }{1 + \sin(x) } = \dfrac{1 - \sin(x) }{ \cos(x) }$

Proof:

Here comes the proof.

Taking LHS,

$\rm \dfrac{ \cos(x) }{1 + \sin(x) }$

$\rm = \dfrac{ \cos(x)(1 - \sin(x)) }{(1 + \sin(x))(1 - \sin(x)) }$

$\rm = \dfrac{ \cos(x)(1 - \sin(x)) }{1 - \sin^{2} (x)}$

Now, We know that,

$\rm \implies \sin^{2}(x) + \cos^{2} (x) = 1$

$\rm \implies \cos^{2} (x) = 1 - \sin ^{2} (x)$

Therefore, on simplifying, we get,

$\rm = \dfrac{ \cos(x)(1 - \sin(x)) }{\cos^{2} (x)}$

$\rm = \dfrac{1 - \sin(x)}{\cos(x)}$

= RHS (Hence Proved)

Formula Used:

• sin²(x) + cos²(x) = 1