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Popular >

sin(x+pi/4)+sin(x-pi/4)+(sqrt(6))/2 =0

Solution

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) + \frac{6}{2} = 0

Solution

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

Solution steps

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) + \frac{6}{2} = 0

Rewrite using trig identities

\frac{3}{2} + 2 sin (x) = 0

Move

\frac{3}{2}

to the right side

2 sin (x) = - \frac{3}{2}

Divide both sides by

2

sin (x) = - \frac{3}{2}

General solutions for

sin (x) = - \frac{3}{2}

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Popular Examples

cos(2x)=((8k-7))/7

cos (2 x) = \frac{( 8 k - 7 )}{7}

cos^2(x)-3sin(2x)+sin^2(x)+2sin^2(2x)=0

cos^{2} (x) - 3 sin (2 x) + sin^{2} (x) + 2 sin^{2} (2 x) = 0

2cos^2(x)+sin(-x)-1=0

2 cos^{2} (x) + sin (- x) - 1 = 0

cos (x) = \frac{- 1}{4}

tan(θ)=sqrt(7/2)

tan (θ) = \frac{7}{2}

Frequently Asked Questions (FAQ)

What is the general solution for sin(x+pi/4)+sin(x-pi/4)+(sqrt(6))/2 =0 ?
The general solution for sin(x+pi/4)+sin(x-pi/4)+(sqrt(6))/2 =0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin