Prove the following trigonomteric identity

Question

How to solve this kind of problem?

(2cos²(-a) / 1-sin(a)) + 2-sin(a) = 2

Answer 1

Identities are true for any a if a is the variable,

do to so with your problem the "2-sin(a)" must mean "2*(-sin(a))"

now cos²(-a)=(1-sin²(-a))=(1-sin(a))*(1+sin(a))

so (2cos²(-a) / 1-sin(a)) + 2*(-sin(a)) = 2

becomes 2*(1+sin(a))-2*sin(a)=2

or 2=2