Question

Simplify cosθ + sinθtanθ.

Answer 1

You should already know that:


`tan\theta = (sin\theta)/(cos\theta)`

Plugging that in we get:


`cos\theta + sin\theta ((sin\theta)/(cos\theta)) =\\\\cos\theta +(sin^2\theta)/(cos\theta)`

Multiply the cos theta by cos theta on the numerator and denominator so we can add them :)


`(cos\theta * (cos\theta)/(cos\theta))+(sin^2\theta)/(cos\theta) = \\\\(cos^2\theta)/(cos\theta) + (sin^2\theta)/(cos\theta)=\\\\(cos^2\theta + sin^2\theta)/(cos\theta)`

You should also know the identity that cos^2 theta + sin^2 theta = 1


`(cos^2\theta + sin^2\theta)/(cos\theta) = \\\\(1)/(cos\theta)`

Therefore,


`cos\theta + sin\theta tan\theta = \boxed{(1)/(cos\theta)}`