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

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

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cos^4(a)+cos^2(a)+sin^2(a)+sin^2(a)=1

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

No Solution for a \in R

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (a) = \frac{3}{2} + \frac{1}{2} i, cos (a) = - \frac{3}{2} - \frac{1}{2} i, cos (a) = - \frac{3}{2} + \frac{1}{2} i, cos (a) = \frac{3}{2} - \frac{1}{2} i

cos (a) = \frac{3}{2} + \frac{1}{2} i :

No Solution

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

No Solution

cos (a) = - \frac{3}{2} + \frac{1}{2} i :

No Solution

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

No Solution

Combine all the solutions

No Solution for a \in R

22 sin (x) + sec (x) = 0

cos (θ) = \frac{- 2}{( 30 + ( 7 ) )}

cos^{3} (x) - 2 sin (x) - 0.7 = 0

cos^{2} (x) - sin^{2} (x) = sec^{2} (x) - csc^{2} (x)

2 - 3 sin (x) = 0

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