Question

Use identities to simplify each expression.
sin(x)+cos^2(x)/sin(x) = ?
tan^3(x)−sec^2(x)tan(x)/cot(−x) = ?
sin^4(x)−cos^4(x) =?

Answer 1

sin + cos^2/sin
= sin + (1-sin^2)/sin
= sin + 1/sin - sin^2/sin
= sin + csc - sin
= csc

tan^3 - sec^2tan/cot(-x)
= tan^3 + sec^2tan^2
= tan^3 + (tan^2+1)tan^2
= tan^4 + tan^3 + tan^2
= tan^2(tan^2+tan+1)
not sure where you want to go with this one

sin^4-cos^4
= (sin^2+cos^2)(sin^2-cos^2)
= -cos(2x)