Question

cosA/1-sinA=1+sinA/cosA​

Answer 1

Answer:

cosA/1-sinA

multiple 1+sinA up and in

cosA(1+sinA)/1-sin²A

cosA(1+sinA)/cos²A

1+sinA/cosA

L.H.S=R.H.S

this is your answer ❣️❣️✌️✌️

Answer 2

Solution:

Given Question:

Prove :  $\dfrac{\cos A}{1- \sin A} = \dfrac{1+\sin A}{\cos\A}$

Step - by - Step Explanation:

$L.H.S:\\\\\dfrac{\cos A}{1- \sin A}$

Mutiply and divide by cos A:

$\dfrac{\cos A}{1- \sin A} \times \dfrac{\cos A}{\cos A}$

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

Put cos²A = 1-sin²A:

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

Apply a² - b² = (a+b)(a-b):

$\dfrac{(1+\sin A)(1 - \sin A)}{(1- \sin A)\cos A}$

Cancel (1-sinA):

$\dfrac{1+\sin A}{\cos A}\\\\=R.H.S$

Hence Proved !!