What is the general solution for cos(3A)+sin(A)=0 ?

The general solution for cos(3A)+sin(A)=0 is A=(pi+4pin)/4 ,A=-(pi+4pin)/8

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cos(3A)+sin(A)=0

cos (3 A) + sin (A) = 0

A = \frac{π + 4 πn}{4}, A = - \frac{π + 4 πn}{8}

Solution steps

cos (3 A) + sin (A) = 0

Subtract

sin (A)

from both sides

cos (3 A) = - sin (A)

Rewrite using trig identities

sin (\frac{π}{2} - 3 A) = sin (- (A))

Apply trig inverse properties

- (A) = \frac{π}{2} - 3 A + 2 πn, - (A) = π - (\frac{π}{2} - 3 A) + 2 πn

- (A) = \frac{π}{2} - 3 A + 2 πn : A = \frac{π + 4 πn}{4}

- (A) = π - (\frac{π}{2} - 3 A) + 2 πn : A = - \frac{π + 4 πn}{8}

A = \frac{π + 4 πn}{4}, A = - \frac{π + 4 πn}{8}

0 = 1 - sec^{2} (x)

sin (θ) = 0.1

\frac{2}{sin ( x )} + 10 = 6

sin (θ) - 0.2 cos (θ) = 0.6377

\frac{1}{sin ( x )} = cos (x)

What is the general solution for cos(3A)+sin(A)=0 ?
The general solution for cos(3A)+sin(A)=0 is A=(pi+4pin)/4 ,A=-(pi+4pin)/8