How do you find the general solutions for $\sqrt{2} tan x = 2 sin x$ $sqrt(2)tan x = 2 sin x$ ?

Question

4799 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-24T21:15:18

Solve $\sqrt{2} tan x = 2 sin x .$ $sqrt2tan x = 2sin x.$

Ans: $0, π; 2 π, and \pm \frac{π}{4}$ $0, pi; 2pi, and +- pi/4$
( $(npi) and (2npi+-pi/4) AA n in ZZ$ )

$sqrt2(sin x/(cos x)) = 2sin x$

$sqrt2sin x = 2sin x *cos x$

$sqrt2sin x - 2sin x *cos x = 0$

$sin x (sqrt2 - 2cos x) = 0$

a. $sin x = 0 -> x = 0; =pi$ , and $x = 2pi$

b. $cos x = sqrt2/2 -> x = +- pi/4$

How do you find the general solutions for sqrt(2)tan x = 2 sin x√2tanx=2sinxsqrt(2)tan x = 2 sin x?