Question

prove that cosA/1-sinA=1+sinA/cosA​

Answer 1

Step-by-step explanation:

don't know it's right or wrong

hope this helps you..

Answer 2

Answer:

Step-by-step explanation:

To Prove :-

$\dfrac{cosA}{1-sinA}=\dfrac{1+sinA}{cosA}$

How To Do :-

By taking the L.H.S and we need to divide and multiply it with '1 + sinA' so that there will be no change in value of the fraction and by using trigonometric identity we can cancel a term and we can prove that L.H.S = R.H.S.

Formula Required :-

sin²A + cos²A = 1

→ cos²A = 1 - sin²A

Solution :-

Taking L.H.S :-

$=\dfrac{cosA}{1-sinA}$

Multiplying and dividing with '1 + sinA' :-

$=\dfrac{cosA}{1-sinA}\times \dfrac{1+sinA}{1+sinA}$

$=\dfrac{cosA(1+sinA)}{(1-sinA)(1+sinA)}$

$=\dfrac{cosA(1+sinA)}{(1)^2-(sinA)^2}$

$=\dfrac{cosA(1+sinA)}{1-sin^2A}$

$=\dfrac{cosA(1+sinA)}{cos^2A}$

[ ∴ 1 - sin²A = cos²A ]

$=\dfrac{1+sinA}{cosA}$

[ ∴ Cancelled both cosA ]

= R.H.S

Hence Proved.