Question

If tan(cot x)=cot(tan x), then sin 2x is equal to:

• A. \(\dfrac{2}{(2n+1)\pi}\)
• B. \(\dfrac{4}{(2n+1)\pi}\)
• C. \(\dfrac{2}{n(n+1)\pi}\)
• D. (4)/(n(n+1)π)

Hint:

Use tan x+cot x=(2)/(\sin2x).

Answer 1

The Correct Option is B

Step 1: Given condition implies: cot x+tan x=(2n+1)(π)/(2)
Step 2: cot x+tan x=(2)/(\sin2x)
Step 3: \sin2x=(4)/((2n+1)π)