What is the general solution for cos^2(x)-sin^2(x)-5sin(x)=3 ?

The general solution for cos^2(x)-sin^2(x)-5sin(x)=3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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cos^2(x)-sin^2(x)-5sin(x)=3

cos^{2} (x) - sin^{2} (x) - 5 sin (x) = 3

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

cos^{2} (x) - sin^{2} (x) - 5 sin (x) = 3

Subtract

3

from both sides

cos^{2} (x) - sin^{2} (x) - 5 sin (x) - 3 = 0

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - 2 :

No Solution

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (θ) = - \frac{21}{5}

t, cos (2 t) - sin (t) = o

cot (x) = - \frac{15}{8}

tan (x^{\circ}) = \frac{30}{73}

cos (x) = (\frac{1}{2})

What is the general solution for cos^2(x)-sin^2(x)-5sin(x)=3 ?
The general solution for cos^2(x)-sin^2(x)-5sin(x)=3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin