Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.
(1 + tan^2 θ) cos^2 θ

Answer 1

\[\left(\frac{\cos^2\theta}{\cos^2\theta} + \frac{\sin^2\theta}{\cos^2 \theta}\right)\cos^2\theta\]

Answer 2

\[\left(\frac{\cos^2\theta + \sin^2\theta}{\cos^2\theta} \right)\cos^2\theta\]

Answer 3

common denominator right?

Answer 4

\[\left(\frac{\cos^2\theta + \sin^2\theta}{\cancel{\cos^2\theta}} \right)\cancel{\cos^2\theta}\]

Answer 5

oic, so will i use the reciprocal identity tan x = sin x/cos x

Answer 6

\[=\cos^2 \theta + \sin^2 \theta \\=1\]

Answer 7

neat thanks for your time