Question

Can anyone help me to verify identities

Answer 1

Explanation:

18.

LHS

`(cos^(2)a-sin^(2)b )/(sin^(2)a.sin^(2)b)`

=
`(cos^(2)a )/(sin^(2)a.sin^(2)b) -(sin^(2)b )/(sin^(2)a.sin^(2)b)`

=
`(cos^(2)a)/(sin^(2)a)` ×
`(1)/(sin^(2)b)` -
`(sin^(2)b)/(sin^(2)b)` ×
`(1)/(sin^(2)a)`

=
`cot^(2)a` ×
`(1+cot^(2)b)` - 1 ×
`(1 + cot^(2)a)`

=
`cot^(2)a` +
`cot^(2)a.cot^(2)b` - 1 -
`cot^(2)a`

=
`cot^(2)a.cot^(2)b` - 1

Then you can conclude that LHS = RHS

19. It's weird. I tried a few ways like simplifying, dividing both numerator and denominator on LHS by tan or sin or cos but it didn't work out.