What is the general solution for solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0 ?

The general solution for solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0 is θ=(2pi)/3+4pin,θ=(10pi)/3+4pin

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solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0

solve for

θ, 4 sin^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) - 7 = 0

θ = \frac{2 π}{3} + 4 πn, θ = \frac{10 π}{3} + 4 πn

Solution steps

4 sin^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) - 7 = 0

Rewrite using trig identities

- 3 - 4 cos^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) = 0

Solve by substitution

cos (\frac{θ}{2}) = \frac{1}{2}, cos (\frac{θ}{2}) = \frac{3}{2}

cos (\frac{θ}{2}) = \frac{1}{2} : θ = \frac{2 π}{3} + 4 πn, θ = \frac{10 π}{3} + 4 πn

cos (\frac{θ}{2}) = \frac{3}{2} :

No Solution

Combine all the solutions

θ = \frac{2 π}{3} + 4 πn, θ = \frac{10 π}{3} + 4 πn

2 sin^{2} (x) - sin (x) = 0, 0 \leq x \leq 2 π

tan (x) = \frac{2}{2}

4 cos (2 x) - 3 = 0

sin^{2} (x) + 1 = 0

cos (t) - sin (2 t) = 0

What is the general solution for solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0 ?
The general solution for solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0 is θ=(2pi)/3+4pin,θ=(10pi)/3+4pin