What is the general solution for 5cos^2(x)+3sin(x)-3=0 ?

The general solution for 5cos^2(x)+3sin(x)-3=0 is x=-0.41151…+2pin,x=pi+0.41151…+2pin,x= pi/2+2pin

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

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

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = arcsin (- \frac{2}{5}) + 2 πn, x = π + arcsin (\frac{2}{5}) + 2 πn, x = \frac{π}{2} + 2 πn

Show solutions in decimal form

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn, x = \frac{π}{2} + 2 πn

\frac{cos ^{2} ( x ) + 1}{1 + cot ^{2} ( x )} = 1

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

1 + cos^{2} (x) = sin^{4} (x)

cos (t) = cos (2 t)

arctan (x + 2) = arcsin (\frac{7}{25}) + arccos (\frac{4}{5})

What is the general solution for 5cos^2(x)+3sin(x)-3=0 ?
The general solution for 5cos^2(x)+3sin(x)-3=0 is x=-0.41151…+2pin,x=pi+0.41151…+2pin,x= pi/2+2pin