Key to "How to simplify the expression sin2tcot⁡2t1−sin2t?"

Kaila Bray

Answered question

2022-12-28

How to simplify the expression

\frac{\sin^{2} t {\cot 2}^{t}}{1 - \sin^{2} t}

Ayden Davidson

Beginner2022-12-29Added 10 answers

\frac{\sin^{2} (t) \cdot \cot^{2} (t)}{1 - \sin^{2} (t)},

not

\frac{\sin^{2} (t) \cdot \cot (2^{t})}{1 - \sin^{2} (t)}

If the first one was what you meant,

\frac{\sin^{2} (t) \cdot \cot^{2} (t)}{1 - \sin^{2} (t)}

(NOTE:

\cot (x) = \frac{\cos (x)}{\sin (x)}

by definition)

= \frac{\sin^{2} (t) \cdot (\frac{\cos^{2} (t)}{\sin^{2} (t)})}{1 - \sin^{2} (t)}

= \frac{\cos^{2} (t)}{1 - \sin^{2} (t)}

(NOTE: use Pythagorean identity

\cos^{2} (x) + \sin^{2} (x) = 1

)

= \frac{\cos^{2} (t)}{\cos^{2} (t)}

= 1

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