# Find all solutions of the equation cos x (2sin x + 1) = 0.?

Updated on August 6, 2022

Find all solutions of the equation cos x (2sin x + 1) = 0.

The answer is A+kpi, B+2kpi and C+2kpi where k is any integer and 0<A<pi, 0<B<C<2pi,

A=?

B=?

C=?

I figured out that A=pi/2

but what does B and C equal? if B is B+2kpi and same for C

so the answer for B was 7pi/6 so Im still trying to figure out C

• cosx(2sinx + 1) = 0 ⇒ (1) cosx = 0 or (2) 2sinx + 1 = 0

(1) cosx = 0 ⇒ x = π/2 + kπ

(2) 2sinx + 1 = 0 ⇒ sinx = -1/2

. . . . . . . . . . . .. ⇒ x = -π/6 + 2kπ or x = π – (-π/6) + 2kπ = 7π/6 + 2kπ

• cos(x)(2sin(x) + 1) = 0

so cos(x) = 0 or sin(x) = -1/2

cos(x) = 0 when x = +/- Ï/2 + 2kÏ

sin(x) = -1/2 when x = -Ï/6 + 2kÏ or 7Ï/6 + 2kÏ

will leave it to you to convert -Ï/2 and -Ï/6 to the proper range

• 0<A<pi

x = pi/2

0<B<C<2pi,

x = pi/2 || x = (7 pi)/6 || x = (3 pi)/2 || x = (11 pi)/6

• This link has a step by step solution to your problem:

http://www.symbolab.com/math/solver/step-by-step/t…

Hope this helps

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