Question

verify the identity: sinθ(cotθ+tanθ)=secθ

Answer 1

Using
\[tanx=\frac{sinx}{cosx}~~~~and~~~~cotx=\frac{1}{tanx}=\frac{cosx}{sinx}\]
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Then,
\[=\sin(x)[\cot(x)+\tan(x)] \\ \\ =\cos(x)[\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}] \\ \\ =\cos(x)+\frac{\sin^2(x)}{\cos(x)}\]
Using \(cos^{2}x=1-sin^2(x)\),
\[=\cos(x)+\frac{1-\cos^2(x)}{\cos(x)} \\ \\ =\cos(x)+\frac{1}{\cos(x)}-\cos(x) \\ \\ =\frac{1}{\cos(x)} \\ \\ =\sec(x)\]

Answer 2

omg that just helped me so much

Answer 3

You're welcome :)

Answer 4

could you help me do some more? @.Sam.

Answer 5

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