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

The general solution for 2cos(a)=3sin^2(a) is a=0.76589…+2pin,a=2pi-0.76589…+2pin

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

2 cos (a) = 3 sin^{2} (a)

a = 0.76589 \dots + 2 πn, a = 2 π - 0.76589 \dots + 2 πn

Solution steps

2 cos (a) = 3 sin^{2} (a)

Subtract

3 sin^{2} (a)

from both sides

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

Rewrite using trig identities

- (1 - cos^{2} (a)) \cdot 3 + 2 cos (a) = 0

Solve by substitution

cos (a) = \frac{- 1 + 10}{3}, cos (a) = - \frac{1 + 10}{3}

cos (a) = \frac{- 1 + 10}{3} : a = arccos (\frac{- 1 + 10}{3}) + 2 πn, a = 2 π - arccos (\frac{- 1 + 10}{3}) + 2 πn

cos (a) = - \frac{1 + 10}{3} :

No Solution

Combine all the solutions

a = arccos (\frac{- 1 + 10}{3}) + 2 πn, a = 2 π - arccos (\frac{- 1 + 10}{3}) + 2 πn

Show solutions in decimal form

a = 0.76589 \dots + 2 πn, a = 2 π - 0.76589 \dots + 2 πn

\frac{11}{cos ( 9 0 ^{\circ} )} = \frac{10}{cos ( x )}

tan^{2} (x) = cot^{2} (x)

x, cos (\frac{x}{2}) = - cos (2 x - 30)

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

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

What is the general solution for 2cos(a)=3sin^2(a) ?
The general solution for 2cos(a)=3sin^2(a) is a=0.76589…+2pin,a=2pi-0.76589…+2pin