Question

[Precalculus] Use trigonometric identities to express:

Answer 1

Remark

Two facts.

1) Tan(x) = Sin(x) / Cos(x)

2) Csc(x) and Sin(x) are reciprocal relationships. When multiplied together, they equal 1.

Solution

So Csc(x) * tan(x) = csc(x) * sin(x) / cos(x) = 1/cos(x) = sec(x)

So far what we have is tan^2(x) + sec(x). We have to get rid of tan^2(x)

Use the identity of 1 + tan^2(x) = sec^2(x)

tan^2(x) = sec^2(x) - 1

sec^2(x) - 1 + sec(x)

a^2 + a - 1   <<<<<< Answer

B is the answer.