What is the general solution for 5cos^2(x)-12sin^2(x)=13 ?

The general solution for 5cos^2(x)-12sin^2(x)=13 is No Solution for x\in\mathbb{R}

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5cos^2(x)-12sin^2(x)=13

5 cos^{2} (x) - 12 sin^{2} (x) = 13

No Solution for x \in R

Solution steps

5 cos^{2} (x) - 12 sin^{2} (x) = 13

Subtract

13

from both sides

5 cos^{2} (x) - 12 sin^{2} (x) - 13 = 0

Rewrite using trig identities

- 8 - 17 sin^{2} (x) = 0

Solve by substitution

sin (x) = i \frac{2 34}{17}, sin (x) = - i \frac{2 34}{17}

sin (x) = i \frac{2 34}{17} :

No Solution

sin (x) = - i \frac{2 34}{17} :

No Solution

Combine all the solutions

No Solution for x \in R

cos^{2} (x) - 0.5 cos (x) = 0

5 sin (x) cos (x) = 2 cos (x)

sin (x) = cos^{3} (x)

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

x, b \cdot f = sin^{3} (x)

What is the general solution for 5cos^2(x)-12sin^2(x)=13 ?
The general solution for 5cos^2(x)-12sin^2(x)=13 is No Solution for x\in\mathbb{R}