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

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

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2cos^2(x)+5sin(x)=5

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

5

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = \frac{3}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{3}{2} :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn

\frac{h ( sin ^{2} ( x ) )}{( cos ( x ) - 1 )} = 0

cos (a) = \frac{- 3}{5}

cos (x) + sin (x - 1) = 0

sin^{22} (x) = \frac{1}{2}

cos^{5} (x) = cos (x)

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