Algebra 2 question

Question

Simplify and enter the trigonometric expression in terms of cosθ

. (Hint: Begin by factoring tanθ

from the last two terms.)

 

cosθ+ sinθ cosθ− tanθ+ tanθsin²θ=?

Answer 1

cosx +sinxcosx -tanx + tanxsin^2x

= cosx +sinxcosx -tanx(1-sin^2x)

= cosx + sinxcosx- (sinx/cosx)(cos^2x)

= cosx + sinxcosx -sinxcosx

= cosx

Answer 2

Hi, in the solution below, we rely on the definition of the tangent as ratio of sine and cosine function and Pythagorean theorem for trigonometry:

cosθ + sinθ cosθ - tanθ + tanθ sin²θ

= cosθ + sinθ cosθ - tanθ (1 - sin²θ)

= cosθ + sinθ cosθ - (sinθ/cosθ) cos²θ

= cosθ + sinθ cosθ - sinθ cosθ = cosθ,

Explanation of steps: First, we factor out tanθ. Second row, we use the tangent definition mentioned above;

next comes the Pythagorean theorem; we then simplify the expression by canceling cosθ. Finally we see that product sinθ cosθ will cancel out with its opposite. The answer is cosθ.