What is the general solution for cos^4(x)+2sin^2(x)+6cos^2(x)+5=0 ?

The general solution for cos^4(x)+2sin^2(x)+6cos^2(x)+5=0 is No Solution for x\in\mathbb{R}

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cos^4(x)+2sin^2(x)+6cos^2(x)+5=0

cos^{4} (x) + 2 sin^{2} (x) + 6 cos^{2} (x) + 5 = 0

No Solution for x \in R

Solution steps

cos^{4} (x) + 2 sin^{2} (x) + 6 cos^{2} (x) + 5 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{3}{2 2 + 7} + \frac{2 + 7}{2} i, cos (x) = - \frac{3}{2 2 + 7} - \frac{2 + 7}{2} i, cos (x) = - \frac{3}{2 2 + 7} + \frac{2 + 7}{2} i, cos (x) = \frac{3}{2 2 + 7} - \frac{2 + 7}{2} i

cos (x) = \frac{3}{2 2 + 7} + \frac{2 + 7}{2} i :

No Solution

cos (x) = - \frac{3}{2 2 + 7} - \frac{2 + 7}{2} i :

No Solution

cos (x) = - \frac{3}{2 2 + 7} + \frac{2 + 7}{2} i :

No Solution

cos (x) = \frac{3}{2 2 + 7} - \frac{2 + 7}{2} i :

No Solution

Combine all the solutions

No Solution for x \in R

1 + sin (2 a) = sin^{2} (a)

\frac{( cos ^{3} ( a ) )}{( 2 cos ^{2} ( a ) - 1 )} = cos (a)

cos (x - 4 5^{\circ}) = 0

7 tan^{2} (x) - 15 = 0

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

What is the general solution for cos^4(x)+2sin^2(x)+6cos^2(x)+5=0 ?
The general solution for cos^4(x)+2sin^2(x)+6cos^2(x)+5=0 is No Solution for x\in\mathbb{R}