Question #004aa

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Answer 1 · 2017-11-20T16:32:22

The two sides are not equivalent.

$(1 - cos (θ)) (1 + sec (θ)) = {sin}^{2} (θ)$ $(1-cos(theta))(1+sec(theta))=sin^2(theta)$

Using FOIL, multiply out the left hand side.

$1 + sec (θ) - cos (θ) - cos (θ) sec (θ)$ $1+sec(theta)-cos(theta)-cos(theta)sec(theta)$

Convert the $sec$ $sec$

$1 + \frac{1}{cos (θ)} - cos (θ) - cos (θ) \frac{1}{cos (θ)}$ $1 +1/cos(theta)-cos(theta)-cos(theta) 1/cos(theta)$

$cancel(1 )+ 1/cos(theta) - cos(theta) - cancel(1)$

$1/cos(theta) - cos^2(theta)/cos(theta)$

$(1-cos^2(theta))/cos(theta)$

$sin^2(theta)/cos(theta)$ or $sin(theta)tan(theta)$

This is not equivalent to the right hand side, $sin^2(theta)$ . You can also see that they are not equivalent by looking at the graphs of both sides.

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