What is the general solution for sin^2(x)+7sin^2(x)+5cos^2(x)+3=0 ?

The general solution for sin^2(x)+7sin^2(x)+5cos^2(x)+3=0 is No Solution for x\in\mathbb{R}

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sin^2(x)+7sin^2(x)+5cos^2(x)+3=0

sin^{2} (x) + 7 sin^{2} (x) + 5 cos^{2} (x) + 3 = 0

No Solution for x \in R

Solution steps

sin^{2} (x) + 7 sin^{2} (x) + 5 cos^{2} (x) + 3 = 0

Rewrite using trig identities

8 + 3 sin^{2} (x) = 0

Solve by substitution

sin (x) = i \frac{2 6}{3}, sin (x) = - i \frac{2 6}{3}

sin (x) = i \frac{2 6}{3} :

No Solution

sin (x) = - i \frac{2 6}{3} :

No Solution

Combine all the solutions

No Solution for x \in R

2 cos (a) = 3 sin^{2} (a)

\frac{11}{cos ( 9 0 ^{\circ} )} = \frac{10}{cos ( x )}

tan^{2} (x) = cot^{2} (x)

x, cos (\frac{x}{2}) = - cos (2 x - 30)

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

What is the general solution for sin^2(x)+7sin^2(x)+5cos^2(x)+3=0 ?
The general solution for sin^2(x)+7sin^2(x)+5cos^2(x)+3=0 is No Solution for x\in\mathbb{R}