Question 6.6.4.7: Establishing an identity Establish the identity: tan v + cot......
Establishing an identity
Establish the identity: {\frac{\tan v+\cot v}{\sec v\csc v}}=1
{\frac{\tan v+\cot v}{\sec v\csc v}} \underset{\overset{\uparrow }{\text{Change to sines and cosines.}}}{=} \frac{\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v}}{\frac{1}{\cos v}\cdot \frac{1}{\sin v}}\underset{\overset{\uparrow }{\text {Add the quotients in the numerator.}}}{=}\frac{\frac{\sin^{2}v+\cos^{2}v}{\cos v\sin v}}{\frac{1}{\cos v \sin v}}
\underset{\overset{\uparrow }{\text{Divide the quotients;} \sin^{2}v+\cos^{2}v=1.}}{=}{\frac{1}{\cos v\sin v}}\cdot{\frac{\cos v\sin v}{1}}=1
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