What is the general solution for (sec^2(a))cos^2(a)=sin^2(a) ?

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

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(sec^2(a))cos^2(a)=sin^2(a)

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

No Solution for a \in R

Solution steps

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

Subtract

sin^{2} (a)

from both sides

sec^{2} (a) cos^{2} (a) - sin^{2} (a) = 0

Factor

sec^{2} (a) cos^{2} (a) - sin^{2} (a) : (sec (a) cos (a) + sin (a)) (sec (a) cos (a) - sin (a))

(sec (a) cos (a) + sin (a)) (sec (a) cos (a) - sin (a)) = 0

Rewrite using trig identities

(- sin (a) + 1) (sin (a) + 1) = 0

Solving each part separately

- sin (a) + 1 = 0 or sin (a) + 1 = 0

- sin (a) + 1 = 0 : a = \frac{π}{2} + 2 πn

sin (a) + 1 = 0 : a = \frac{3 π}{2} + 2 πn

Combine all the solutions

a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

No Solution for a \in R

- 2 sin (x) + 5 sin^{2} (x) = 0

3 \cdot tan^{2} (x) - 1 = 0

cos^{4} (x) = \frac{sin ^{2} ( x ) - 1}{4}

2 \cdot sin (x) + 1 = 0

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

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