Question

1+sin(a)/1+csc(a)=tan(a)/sec(a)

Answer 1

Below.

Explanation:

( 1 + sin a) / (1 + csc a)

= (1 + sin a ) /( 1 + 1/ sin a)

= ( 1 + sin a) / (sin a + 1)/ (sin a)

= (sin a(1 + sin a)) / (1 + sin a)

= sin a.

tan a / sec a

= (sin a / cos a) / (1 /cos a)

= (sin a cos a) / cos a

= sin a

The two expressions are both equal to sin a:

Therefore

(1 + sin a) /( 1 + csc a) = tan a / sec a.