How do you verify the identity sin⁡2xsin⁡x=2sec⁡x?

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Mary Goodson · Accepted Answer

Have a look:  sin⁡(2x)=2sin⁡(x)cos⁡(x)  sec⁡(x)=1cos⁡(x)  ⇒2sin⁡(x)cos⁡(x)sin⁡(x)  =21cos⁡(x)  ⇒2cos⁡(x)=2cos⁡(x)

Thomas White · Accepted Answer

Сan you please a solution with a detailed explanation

RizerMix · Accepted Answer

Verify the following identity: sin⁡(2x)/sin⁡(x)=2/sec⁡(x) Eliminate the denominators on both sides. Cross multiply: sec⁡(x)sin⁡(2x)=?2sin⁡(x) Express the left hand side in terms of sine and cosine. Write secant as 1/cos: 1/cos⁡(x)sin⁡(2x)=?2sin⁡(x) Eliminate the denominator on the left hand side. Multiply both sides by cos⁡(x): sin⁡(2x)=?2cos⁡(x)sin⁡(x) Use the double angle identity on sin⁡(2x) sin⁡(2x)=2sin⁡(x)cos⁡(x): 2cos⁡(x)sin⁡(x)=?2cos⁡(x)sin⁡(x) Come to a conclusion. The left hand side and right hand side are identical: (identity has been verified)

How do you verify the identity \frac{\sin 2x}{\sin x}=\frac{2}{\sec x}?

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