Question

cosA/1+sinA+1+sinA/cosA=2secA​

Answer 1

Step-by-step explanation:

cos A/(1+sinA) + (1+sinA)/cosA

= cosA(1-sinA)/(1-sin^2A) + sec A + tan A

= cosA(1-sinA)/cos^2A + secA + tan A

= (1-sinA)/cosA + sec A + tan A

= sec A - tan A + sec A + tan A

= 2 sec A

Answer 2

Step-by-step explanation:

To prove :-

Cos A / ( 1 + sin A ) + (1 + sin A ) / cos A = 2 sec A

Proof :-

Solving LHS we have ,

Cos A / ( 1 + sin A ) + ( 1 + sin A ) / cos A

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

={cos²A + (1+sinA)²} /cosA (1+sinA)

={cos²A+ 1+ sin²A+2 sinA }/cosA (1+sinA)

We will use an identity here , the indentity is ( sin²∅ +cos²∅ =1 )

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

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

=2/cosA

=2secA = RHS

Hence , we have proved the given equation .