Question

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

Answer 1

sin(x) = 2cos(x)
tan(x) = 2
tan⁻¹[tan(x)] = tan⁻¹(2)
x ≈ 63.4

sin(2x) = sin[2(63.4)]
sin(2x) = sin(126.8)
sin(2x) ≈ 0.801

Answer 2

Sin2x = 0.801

Explanation:

Given : sinx = 2cosx .

To find : what is the value of sin2x.

Solution : We have given

sinx = 2cosx .

On dividing both sides by cos x

`(sinx)/(cosx)` = 2 .

tan x = 2

Taking inverse of tanx .

x =
`Tan^(-1)(2)`.

x = 63.43

We need to find Sin2x .

Sin2x = Sin2(63.43)

Sin2x = Sin ( 126.86).

Sin2x = 0.801

Therefore, Sin2x = 0.801