What is the general solution for 4-7sin(x)=cos^2(x) ?

The general solution for 4-7sin(x)=cos^2(x) is x=0.47644…+2pin,x=pi-0.47644…+2pin

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4-7sin(x)=cos^2(x)

4 - 7 sin (x) = cos^{2} (x)

x = 0.47644 \dots + 2 πn, x = π - 0.47644 \dots + 2 πn

Solution steps

4 - 7 sin (x) = cos^{2} (x)

Subtract

cos^{2} (x)

from both sides

4 - 7 sin (x) - cos^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{7 + 37}{2}, sin (x) = \frac{7 - 37}{2}

sin (x) = \frac{7 + 37}{2} :

No Solution

sin (x) = \frac{7 - 37}{2} : x = arcsin (\frac{7 - 37}{2}) + 2 πn, x = π - arcsin (\frac{7 - 37}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{7 - 37}{2}) + 2 πn, x = π - arcsin (\frac{7 - 37}{2}) + 2 πn

Show solutions in decimal form

x = 0.47644 \dots + 2 πn, x = π - 0.47644 \dots + 2 πn

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

\frac{5}{tan ( x )} = - 2

tan^{22} (x) = sec^{2} (x) - 1

tan^{4} (x) + tan^{2} (x) = tan (x)

sin^{4} (x) + sin^{2} (x) = sin^{6} (x)

What is the general solution for 4-7sin(x)=cos^2(x) ?
The general solution for 4-7sin(x)=cos^2(x) is x=0.47644…+2pin,x=pi-0.47644…+2pin