What is the general solution for cos(5t)cos(2t)=-sin(5t)sin(2t) ?

The general solution for cos(5t)cos(2t)=-sin(5t)sin(2t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3

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cos(5t)cos(2t)=-sin(5t)sin(2t)

cos (5 t) cos (2 t) = - sin (5 t) sin (2 t)

t = \frac{π}{6} + \frac{2 πn}{3}, t = \frac{π}{2} + \frac{2 πn}{3}

Solution steps

cos (5 t) cos (2 t) = - sin (5 t) sin (2 t)

Subtract

- sin (5 t) sin (2 t)

from both sides

cos (5 t) cos (2 t) + sin (5 t) sin (2 t) = 0

Rewrite using trig identities

cos (5 t - 2 t) = 0

General solutions for

cos (5 t - 2 t) = 0

5 t - 2 t = \frac{π}{2} + 2 πn, 5 t - 2 t = \frac{3 π}{2} + 2 πn

Solve

5 t - 2 t = \frac{π}{2} + 2 πn : t = \frac{π}{6} + \frac{2 πn}{3}

Solve

5 t - 2 t = \frac{3 π}{2} + 2 πn : t = \frac{π}{2} + \frac{2 πn}{3}

t = \frac{π}{6} + \frac{2 πn}{3}, t = \frac{π}{2} + \frac{2 πn}{3}

x, cos (x) = sin (y)

tan (θ) = \frac{5}{8}

3 cos^{2} (x) = 9 sin (x) + 9

cos^{2} (x) - 2 cos (x) = 3

cos^{2} (x) = sin (x) + sin^{2} (x)

What is the general solution for cos(5t)cos(2t)=-sin(5t)sin(2t) ?
The general solution for cos(5t)cos(2t)=-sin(5t)sin(2t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3