What is the general solution for 1+sin^2(x)+cos^4(x)=0 ?

The general solution for 1+sin^2(x)+cos^4(x)=0 is No Solution for x\in\mathbb{R}

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1+sin^2(x)+cos^4(x)=0

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

No Solution for x \in R

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{7}{2 2 2 - 1} + \frac{2 2 - 1}{2} i, cos (x) = - \frac{7}{2 ^{2} \cdot \frac{2 2 - 1}{2}} - \frac{2 2 - 1}{2} i, cos (x) = - \frac{7}{2 2 2 - 1} + \frac{2 2 - 1}{2} i, cos (x) = - \frac{7}{2 ( - 2 2 - 1 )} - \frac{2 2 - 1}{2} i

cos (x) = \frac{7}{2 2 2 - 1} + \frac{2 2 - 1}{2} i :

No Solution

cos (x) = - \frac{7}{2 ^{2} \cdot \frac{2 2 - 1}{2}} - \frac{2 2 - 1}{2} i :

No Solution

cos (x) = - \frac{7}{2 2 2 - 1} + \frac{2 2 - 1}{2} i :

No Solution

cos (x) = - \frac{7}{2 ( - 2 2 - 1 )} - \frac{2 2 - 1}{2} i :

No Solution

Combine all the solutions

No Solution for x \in R

7 \cdot sin^{2} (x) + cos^{2} (x) - 1 = 6 sin (x)

4 sec^{2} (x) - 3 tan^{2} (x) = 5 tan^{2} (x)

cos^{3} (x) = 66

23 \cdot sin (4 x + 6 0^{0}) - 3 = 0

\frac{sin ( x ) + sin ^{2} ( x )}{2} = 0.5

What is the general solution for 1+sin^2(x)+cos^4(x)=0 ?
The general solution for 1+sin^2(x)+cos^4(x)=0 is No Solution for x\in\mathbb{R}