Question

prove that Cos A by 1 + sin a + 1 + sin a by cos A is equals to 2 secant a

Answer 1

Answer:-

I assume the grouping is

cos/(1 + sin) + (1 + sin)/cos = 2 sec common denominator is cos(1 + sin)

[ cos · cos + (1 + sin)(1 + sin) ] / [cos(1 + sin)] = 2 sec

[ cos2 + sin2 + 2 sin + 1 ] / [cos(1 + sin)] = 2 sec

[ 1 + 2 sin + 1] / [cos(1 + sin)] = 2 sec

[ 2 sin + 2] / [cos(1 + sin)] = 2 sec

[ 2(sin + 1] / [cos(1 + sin)] = 2 sec

2 1/cos = 2 sec

2 sec = 2sec.

⚡Hope it will help you.⚡

Answer 2

solution:

LHS.

cos a/1+sin a+1+sin a/cos a

cos²a+(1+sin a)²/(1+sin a) cos a

cos²a+1+2sin a+sin²a/(1+sin a)cos a

2+2sin a/(1+sin a)cos a

2(1+sin a)/cos a(1+sin a)

=2/cos a=2sec a=RHS.

hope ! i have helped u.