need answer quickly! thank you in advance!

Answer:b)(b²-a²)Step-by-step explanation:a cotθ + b cosecθ =pb cotθ + a cosecθ =qNow,p²- q²=(a cotθ + b cosecθ)² - (b cotθ + a cosecθ)²     [a²-b²=(a+b)(a-b)]=(acotθ+bcosecθ + bcotθ+ acosecθ) (a cotθ + bcosecθ -bcotθ-acosecθ)={a(cotθ+cosecθ)+b(cotθ+cosecθ)} {a (cotθ-cosecθ)+b (cosecθ-cotθ)}={a(cotθ+cosecθ)+b(cotθ+cosecθ)} [a (cotθ-cosecθ) + {- b (cotθ-cosecθ)} ]={a(cotθ+cosecθ)+b(cotθ+cosecθ)} {a (cotθ-cosecθ) - b (cotθ-cosecθ)}={(cotθ+cosecθ)(a+b)} {(cotθ-cosecθ) (a-b)}=(cotθ+cosecθ) (a+b) (cotθ-cosecθ) (a-b)=(cotθ+cosecθ) (cotθ-cosecθ) (a+b) (a-b)        = (cot²θ-cosec²θ) (a²-b²)                                 [(a+b) (a-b)= (a²-b²)]= -1 . (a²-b²)                               [ 1+cot²θ=cosec²θ ; ∴cot²θ-cosec²θ=-1] =(b²-a²)