Trigonometry, Trigonometric Identities

Question

I need help answering this question.

(sin/cos) + (cos/sin) = csc sec

Answer 1

Lets work on the left side of the equation. Combine the 2 fractions with a common denominator of (sinx)(cosx)with gives us

(sin^2x+cos^2x)/ (sinx)(cosx) use the identity sin^2x +cos^2= 1 to give you

1/(sinx0(cosx) which is the same as (1/sin)(1/cosx)

1/sinx = csc x and 1/cosx = secx

(cscx) (secx0 = (cscx) (secx)

Answer 2

(sin x/cos x) + (cos x/sin x) Get a common denominator

(sin x/sin x)(sin x/cos x) + (cos x/sin x)(cos x/cos x) Simplify

(sin²x+cos²x)/(sin x cos x) Apply the trig identity to the numerator sin²x+cos²x=1

1/(sin x cos x) Apply reciprocals

csc x sec x = csc x sec x