Question

Complete the identity:
Please see attached photo.

Answer 1

Answer:
2csc^2(Θ) - 1

Step-by-step explanation:
The given is:
(1 + cos^2(Θ)) / sin^2(Θ)
Now,
sin^2 (Θ) + cos^2(Θ) = 1
This means that:
cos^2(Θ) = 1 - sin^2 (Θ) ...........> I

Substitute with I in the given equation, this will lead to:
(1+1-sin^2 (Θ) ) / sin^2(Θ)
(2-sin^2 (Θ) ) / sin^2(Θ)

This expression can be written as:
[2/sin^2(Θ)] - [sin^2 (Θ) / sin^2(Θ)]

This is equivalent to:
2csc^2(Θ) - 1

Hope this helps :)