What is the general solution for cos(2x-a)=sin(3x) ?

The general solution for cos(2x-a)=sin(3x) is x=(pi+2a+4pin)/(10),x=pi-pi/2-a+2pin

Popular >

cos(2x-a)=sin(3x)

cos (2 x - a) = sin (3 x)

x = \frac{π + 2 a + 4 πn}{10}, x = π - \frac{π}{2} - a + 2 πn

Solution steps

cos (2 x - a) = sin (3 x)

Rewrite using trig identities

cos (2 x - a) = sin (\frac{π}{2} - (2 x - a))

Apply trig inverse properties

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

3 x = \frac{π}{2} - (2 x - a) + 2 πn : x = \frac{π + 2 a + 4 πn}{10}

3 x = π - (\frac{π}{2} - (2 x - a)) + 2 πn : x = π - \frac{π}{2} - a + 2 πn

x = \frac{π + 2 a + 4 πn}{10}, x = π - \frac{π}{2} - a + 2 πn

x, 2 cos (x) = 3

41 sin^{2} (x) + 32 sin (x) - 9 = 0

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

sin (θ) - 3 cos (θ) = 2

sec^{2} (3 θ) cos^{2} (3 θ) = sec^{2} (3 θ) + cos^{2} (3 θ)

What is the general solution for cos(2x-a)=sin(3x) ?
The general solution for cos(2x-a)=sin(3x) is x=(pi+2a+4pin)/(10),x=pi-pi/2-a+2pin