Key to "Verify the identify. 1+csc⁡3βsec⁡3β−cot⁡3β=cos⁡3β"

beljuA

Answered question

2021-09-11

Verify the identify.

\frac{1 + \csc 3 β}{\sec 3 β} - \cot 3 β = \cos 3 β

Jozlyn

Skilled2021-09-12Added 85 answers

Solution:

L H S = \frac{1 + \csc 3 β}{\sec 3 β} - \cot 3 β

= \frac{1 + \frac{1}{\sin 3 β}}{\frac{1}{\cos 3 β}} - \frac{\cos 3 β}{\sin 3 β}

= \frac{\frac{\sin 3 β + 1}{\sin 3 β}}{\frac{1}{\cos 3 β}} - \frac{\cos 3 β}{\sin 3 β}

= \frac{\cos 3 β}{\sin 3 β} (\sin 3 β + 1) - \frac{\cos 3 β}{\sin 3 β}

= \frac{\cos 3 β [\sin 3 β + 1 - 1]}{\sin 3 β}

= \cos 3 β \frac{[\sin 3 β]}{\sin 3 β}

= \cos 3 β

= R H S

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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