What is the general solution for 2cos^2(x)+11sin(x)=7 ?

The general solution for 2cos^2(x)+11sin(x)=7 is x= pi/6+2pin,x=(5pi)/6+2pin

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2cos^2(x)+11sin(x)=7

2 cos^{2} (x) + 11 sin (x) = 7

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

Solution steps

2 cos^{2} (x) + 11 sin (x) = 7

Subtract

7

from both sides

2 cos^{2} (x) + 11 sin (x) - 7 = 0

Rewrite using trig identities

- 5 + 11 sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 5

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

sin (x) = 5 :

No Solution

Combine all the solutions

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

cos (x) csc (x) = 2 cos (x)

cot (x) = \frac{1}{3}

2 sin (3 x - \frac{π}{3}) = - 3, 0 \leq x \leq 2 π

sin (x) = 2 \cdot sin (3 x)

tan^{2} (x) - 5 tan (x) - 6 = 0

What is the general solution for 2cos^2(x)+11sin(x)=7 ?
The general solution for 2cos^2(x)+11sin(x)=7 is x= pi/6+2pin,x=(5pi)/6+2pin