Simplify \frac{\sec^2 \theta-\cos^2 \theta}{\tan^2 \theta} My workings: \frac {\sec^2\theta - \cos^2\theta}{\tan^2\theta}=\frac {\frac

Naima Cox

Naima Cox

Answered question

2022-01-28

Simplify sec2θcos2θtan2θ
My workings:
sec2θcos2θtan2θ=1cos2θcos2θtan2θ

Answer & Explanation

Emilie Booker

Emilie Booker

Beginner2022-01-29Added 14 answers

sec2θcos2θtan2θ
=1cos2θcos2θtan2θ
From here, use the common denominator cos2θ
=1cos2θcos4θcos2θtan2θ
=1cos4θcos2θtan2θ=(1cos2θ)(1+cos2θ)cos2θtan2θ=(1cos2θ)(1+cos2θ)cos2θsin2θcos2θ={(1cos2θ)(1+cos2θ)}sin2θ
Recall 1cos2θ=sin2θ
={(sin2θ)(1+cos2θ)}sin2θ=1+cos2θ
Larissa Hogan

Larissa Hogan

Beginner2022-01-30Added 10 answers

For cosθ0 we have
cos2θcos2θ1cos2θcos2θtan2θ=1cos4θsin2θ=(1cos2θ)(1+cos2θ)1cos2θ=1+cos2θ

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