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Alex_Xolod [135]
3 years ago
13

Simplify sin q + cosq cotq.

Mathematics
1 answer:
IRINA_888 [86]3 years ago
3 0
\sin q+\cos q\cot q=\sin q+\cos q\cdot\dfrac{\cos q}{\sin q}=\sin q+\dfrac{\cos^2q}{\sin q}\\\\=\dfrac{sin^2q}{\sin q}+\dfrac{\cos^2q}{\sin q}=\dfrac{\sin^2q+\cos^2q}{\sin q}=\dfrac{1}{\sin q}=\csc q\\\\Used:\\\cot q=\dfrac{\cos q}{\sin q}\\\\\sin^2q+\cos^2q=1\\\\\csc q=\dfrac{1}{\sin q}
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