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

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Answer 1 · 2015-10-24T21:15:18

Solve #sqrt2tan x = 2sin x.#

Ans: #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#