What is the general solution for cos(9x+15)=sin(7x-5) ?

The general solution for cos(9x+15)=sin(7x-5) is x=(4pin+pi-20}{32},x=-\frac{4pin+40+pi)/4

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cos(9x+15)=sin(7x-5)

cos (9 x + 15) = sin (7 x - 5)

x = \frac{4 πn + π - 20}{32}, x = - \frac{4 πn + 40 + π}{4}

Solution steps

cos (9 x + 15) = sin (7 x - 5)

Rewrite using trig identities

cos (9 x + 15) = sin (\frac{π}{2} - (9 x + 15))

Apply trig inverse properties

7 x - 5 = \frac{π}{2} - (9 x + 15) + 2 πn, 7 x - 5 = π - (\frac{π}{2} - (9 x + 15)) + 2 πn

7 x - 5 = \frac{π}{2} - (9 x + 15) + 2 πn : x = \frac{4 πn + π - 20}{32}

7 x - 5 = π - (\frac{π}{2} - (9 x + 15)) + 2 πn : x = - \frac{4 πn + 40 + π}{4}

x = \frac{4 πn + π - 20}{32}, x = - \frac{4 πn + 40 + π}{4}

3 cos (2 θ) - sin (θ) = 1

\frac{1}{2} - sin (x) = 1

sin (t) + 2 = 3

tan (3 θ) = - 1

1 + 2 sin (2 x) = 0

What is the general solution for cos(9x+15)=sin(7x-5) ?
The general solution for cos(9x+15)=sin(7x-5) is x=(4pin+pi-20}{32},x=-\frac{4pin+40+pi)/4