Question

CosA/1-sinA +1-sinA/cosA =2secA​

Answer 1

Step-by-step explanation:

Given cosA/(1+sinA) +(1+sinA)/cosA

On taking the LCM we get,

={cos²A +(1+sinA)²}/cosA.(1+sinA)

Combining the like terms and adding and also we know that,use sin²A+cos²A =1

=(1+1+2sinA)/cosA(1+sinA)

=2(1+sinA)/cosA(1+sinA)

=2/cosA

=2secA

Hence Proved

Answer 2

$\frac{cosa}{1 - sina} + \frac{1 - sina}{cosa} \\ \\ = \frac{ {cos}^{2}a + ( {1 - sina})^{2} }{(1 - sina)cosa} \\ \\ = \frac{ {cos}^{2}a + 1 + {sin}^{2} a - 2sina }{(1 - sina)cosa} \\ \\ = \frac{2 - 2sina}{(1 - sina)cosa} \\ \\ = \frac{2}{cosa} \\ \\ = 2seca$