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

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

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4sin^2(θ/2)+8cos(θ/2)-7=0

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

11 sin (x) + 5 = sin (x)

cos (x) = 2 sin (x)

- 16 sin (4 x) = 0

3 tan (θ) + 1 = 0

2 tan^{2} (x) = 3 sec (x)

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