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

The general solution for 4sin^2(x)+cos(x)=7 is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Subtract

7

from both sides

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

Rewrite using trig identities

- 3 + cos (x) - 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{1}{8} - i \frac{47}{8}, cos (x) = \frac{1}{8} + i \frac{47}{8}

cos (x) = \frac{1}{8} - i \frac{47}{8} :

No Solution

cos (x) = \frac{1}{8} + i \frac{47}{8} :

No Solution

Combine all the solutions

No Solution for x \in R

sin (A) = 0.4

3 sin^{2} (θ) - 3 = 0

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

sin (x) = \frac{17}{8}

3 csc (θ) = 2

What is the general solution for 4sin^2(x)+cos(x)=7 ?
The general solution for 4sin^2(x)+cos(x)=7 is No Solution for x\in\mathbb{R}