What is the general solution for sin^2(x)sec(x)cot(x)=(sqrt(3))/2 ?

The general solution for sin^2(x)sec(x)cot(x)=(sqrt(3))/2 is x= pi/3+2pin,x=(2pi)/3+2pin

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sin^2(x)sec(x)cot(x)=(sqrt(3))/2

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

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

Solution steps

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

Subtract

\frac{3}{2}

from both sides

sin^{2} (x) sec (x) cot (x) - \frac{3}{2} = 0

Simplify

sin^{2} (x) sec (x) cot (x) - \frac{3}{2} : \frac{2 sin ^{2} ( x ) sec ( x ) cot ( x ) - 3}{2}

\frac{2 sin ^{2} ( x ) sec ( x ) cot ( x ) - 3}{2} = 0

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

2 sin^{2} (x) sec (x) cot (x) - 3 = 0

Express with sin, cos

- 3 + 2 sin (x) = 0

Move

3

to the right side

2 sin (x) = 3

Divide both sides by

2

sin (x) = \frac{3}{2}

General solutions for

sin (x) = \frac{3}{2}

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

x, sin (y) = y cos (2 x)

2 sin (\frac{π}{2} - θ) = sin (- θ)

csc (x) cot (x) + cot (x) = 0

tan (x) = \frac{50}{36}

- 2 + cot (x) = - 3

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