Question

Can someone please help me verify each identity

Answer 1

see explanation

Explanation:

combine the fractions on the left side into a single expression

I will use x instead of theta- I can't get it in the fraction

`(sin^2x+(1+cosx)^2)/(sinx(1+cosx))`

=
`(sin^2x+1+2cosx+cos^2x)/(sinx(1+cosx))`

[ note that sin²x + cos²x = 1 ]

=
`(2+2cosx)/(sinx(1+cosx))`

=
`(2(1+cosx))/(sinx(1+cosx)`

=
`(2)/(sinx)`

= 2cscx = right side ⇒ verified