Question

express (tan t + sin t) / (1+sec t) in terms of a single trig function

Trigonometric Functions
ANSWERED
asked 2021-05-03
express \(\displaystyle\frac{{{\tan{{t}}}+{\sin{{t}}}}}{{{1}+{\sec{{t}}}}}\) in terms of a single trig function

Expert Answers (1)

2021-05-04

We are given: \(\displaystyle\frac{{{\tan{{t}}}+{\sin{{t}}}}}{{{1}+{\sec{{t}}}}}\)
Express using sine and cosine: \(=\frac{\left(\frac{\sin t}{\cos t}\right)+\sin t}{1+\left(\frac{1}{\cos t}\right)} =\frac{\frac{(\sin t+\sin t \cos t)}{\cos t}}{\frac{\cos t+1}{ \cos t}} =\frac{\sin t+\sin t \cos t}{\cos t+1}\)
Factor out sint: \(\displaystyle={\sin{{t}}}\frac{{{1}+{\cos{{t}}}}}{{{\cos{{t}}}+{1}}}\)
Cancel \(1+\cos tt: =\sin t\)

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