What is the general solution for cos(2x)=8-15sin(x) ?

The general solution for cos(2x)=8-15sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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cos(2x)=8-15sin(x)

cos (2 x) = 8 - 15 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

cos (2 x) = 8 - 15 sin (x)

Subtract

8 - 15 sin (x)

from both sides

cos (2 x) - 8 + 15 sin (x) = 0

Rewrite using trig identities

- 7 + 15 sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 7

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 7 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (4 x) = cos (\frac{x}{2})

a, cos (a - b) = 2

cos (\frac{π}{2} - x) tan (x) - sec (- x) = 1

\frac{cot ( θ ) + csc ( θ )}{sec ( θ ) + 1} = sin (θ)

2 = cos^{2} (x)

What is the general solution for cos(2x)=8-15sin(x) ?
The general solution for cos(2x)=8-15sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin