Question

Sin a + cos a/sec a+ cosec a= sin a* cos a

Answer 1

See proof below

Explanation:

sin a + cos a/sec a+ cosec a= sin a* cos a

(sina+cosa)/(sec a + cosec a)

In trigonometry identity

seca = 1/cos a

cosec a = 1/sin a

Substituted into the given expression

= sina + cosa/(1/cosa+1/sina)

Find the LCM

= sina + cosa /(sina+cosa/sinacosa)

= (sina+cosa) * sinacosa/(sina + cosa)

= sinacosa (RHS)

This shows that the equation is true