What is the general solution for sin(x-(5pi)/3)+sin(x+(5pi)/3)=1 ?

The general solution for sin(x-(5pi)/3)+sin(x+(5pi)/3)=1 is x= pi/2+2pin

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sin(x-(5pi)/3)+sin(x+(5pi)/3)=1

sin (x - \frac{5 π}{3}) + sin (x + \frac{5 π}{3}) = 1

x = \frac{π}{2} + 2 πn

Solution steps

sin (x - \frac{5 π}{3}) + sin (x + \frac{5 π}{3}) = 1

Rewrite using trig identities

sin (x) = 1

General solutions for

sin (x) = 1

x = \frac{π}{2} + 2 πn

- sec (\frac{x}{2}) = 2 csc (\frac{x}{2})

sec^{2} (θ) - sec (θ) = 2, θ [0, \frac{π}{2}]

x, sin (x) = - 0.5

tan (2 θ) = 1, 0 \leq θ \leq 2 π

0.4 = 0.4 cos^{2} (θ)

What is the general solution for sin(x-(5pi)/3)+sin(x+(5pi)/3)=1 ?
The general solution for sin(x-(5pi)/3)+sin(x+(5pi)/3)=1 is x= pi/2+2pin