What is the general solution for 3(cos^2(a))/(sin^2(a))=(cot(a))^2 ?

The general solution for 3(cos^2(a))/(sin^2(a))=(cot(a))^2 is a= pi/2+2pin,a=(3pi)/2+2pin

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3(cos^2(a))/(sin^2(a))=(cot(a))^2

3 \frac{cos ^{2} ( a )}{sin ^{2} ( a )} = (cot (a))^{2}

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

Solution steps

3 \cdot \frac{cos ^{2} ( a )}{sin ^{2} ( a )} = (cot (a))^{2}

Subtract

(cot (a))^{2}

from both sides

\frac{3 cos ^{2} ( a )}{sin ^{2} ( a )} - cot^{2} (a) = 0

Simplify

\frac{3 cos ^{2} ( a )}{sin ^{2} ( a )} - cot^{2} (a) : \frac{3 cos ^{2} ( a ) - cot ^{2} ( a ) sin ^{2} ( a )}{sin ^{2} ( a )}

\frac{3 cos ^{2} ( a ) - cot ^{2} ( a ) sin ^{2} ( a )}{sin ^{2} ( a )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factor

3 cos^{2} (a) - cot^{2} (a) sin^{2} (a) : (3 cos (a) + cot (a) sin (a)) (3 cos (a) - cot (a) sin (a))

(3 cos (a) + cot (a) sin (a)) (3 cos (a) - cot (a) sin (a)) = 0

Solving each part separately

3 cos (a) + cot (a) sin (a) = 0 or 3 cos (a) - cot (a) sin (a) = 0

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

3 cos (a) - cot (a) sin (a) = 0 : a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

cos (x) = \frac{- 2}{2}

tan (x) = - 0.22

θ, 1 + cos (θ) = 3 cos (θ)

3 sin (x) - 4 cos (x) = 0

sin (θ) = \frac{1}{4}, 0^{\circ} < θ < 9 0^{\circ}

What is the general solution for 3(cos^2(a))/(sin^2(a))=(cot(a))^2 ?
The general solution for 3(cos^2(a))/(sin^2(a))=(cot(a))^2 is a= pi/2+2pin,a=(3pi)/2+2pin