"Express in terms of sin x: cot2x−1csc2x" was answered by students like you

Bevan Mcdonald

Answered question

2020-12-01

Express in terms of sin x:

\frac{\cot^{2} x - 1}{\csc^{2} x}

bahaistag

Skilled2020-12-02Added 100 answers

\frac{\cot^{2} (x) - 1}{\csc^{2} (x)}

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

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

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

= \cos^{2} (x) - \sin^{2} (x)

= (1 - \sin^{2} (x)) - \sin^{2} (x)

= 1 - 2 \sin^{2} (x)

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