What is the general solution for sin(15x)+cos(15x)=0 ?

The general solution for sin(15x)+cos(15x)=0 is x= pi/(20)+(pin)/(15)

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sin(15x)+cos(15x)=0

sin (15 x) + cos (15 x) = 0

x = \frac{π}{20} + \frac{πn}{15}

Solution steps

sin (15 x) + cos (15 x) = 0

Rewrite using trig identities

tan (15 x) + 1 = 0

Move

1

to the right side

tan (15 x) = - 1

General solutions for

tan (15 x) = - 1

15 x = \frac{3 π}{4} + πn

Solve

15 x = \frac{3 π}{4} + πn : x = \frac{π}{20} + \frac{πn}{15}

x = \frac{π}{20} + \frac{πn}{15}

1 + 2 sin (\frac{t ^{2}}{2}) = 0

3 tan^{2} (x) - 2 = csc^{2} (x) - cot^{2} (x)

sin (3 θ) = - \frac{3}{2}

x, arctan (\frac{y}{x}) = 0

cos (x) = - 1, 0 \leq x < 2 π

What is the general solution for sin(15x)+cos(15x)=0 ?
The general solution for sin(15x)+cos(15x)=0 is x= pi/(20)+(pin)/(15)