What is the general solution for 4cos^2(x)+6=7 ?

The general solution for 4cos^2(x)+6=7 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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4cos^2(x)+6=7

4 cos^{2} (x) + 6 = 7

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

4 cos^{2} (x) + 6 = 7

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

sec (θ) - 1 = (2 - 1) tan (θ)

cos (a) = - \frac{4}{5}

2 tan (θ) - sec (θ) = 0

sin (θ) = \frac{175}{214}

2 \cdot cos^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq π

What is the general solution for 4cos^2(x)+6=7 ?
The general solution for 4cos^2(x)+6=7 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin