Question

If sinx=2cosx Then, what is the value of sin2x?

Answer 1

x = inv tan (2)

Answer 2

But answer is 4/5.Why?

Answer 3

\[\sin(2x) = 2\sin(x) \cos(x)\]
replace sin(x) with 2cos(x)
\[\sin(2x) = 4\cos^{2} (x)\]
solve for cos^2 using triangle

yields
cos^2 = 1/5
\[\rightarrow \sin(2x) = 4*\frac{1}{5} = \frac{4}{5}\]