What is the general solution for 10sin(x)=4cos^2(x)+2 ?

The general solution for 10sin(x)=4cos^2(x)+2 is x= pi/6+2pin,x=(5pi)/6+2pin

Popular >

10sin(x)=4cos^2(x)+2

10 sin (x) = 4 cos^{2} (x) + 2

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

10 sin (x) = 4 cos^{2} (x) + 2

Subtract

4 cos^{2} (x) + 2

from both sides

10 sin (x) - 4 cos^{2} (x) - 2 = 0

Rewrite using trig identities

- 6 + 10 sin (x) + 4 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 3

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

- 4 + sin (- 3 x + \frac{2 π}{3}) = - 4

2 \cdot sin (x) \cdot cos (x) = cos (x)

sin (2 θ) = \frac{- 2 6}{7}

x, sin (x) = - \frac{7}{25}

\frac{1}{tan ( α )} + tan (α) = \frac{1}{sin ( α )}

What is the general solution for 10sin(x)=4cos^2(x)+2 ?
The general solution for 10sin(x)=4cos^2(x)+2 is x= pi/6+2pin,x=(5pi)/6+2pin