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sin(x)sin(2x)-cos(x)cos(2x)=(sqrt(3))/2

Solution

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

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

Solution steps

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

Rewrite using trig identities

- cos (x + 2 x) = \frac{3}{2}

Divide both sides by

- 1

cos (x + 2 x) = - \frac{3}{2}

General solutions for

cos (x + 2 x) = - \frac{3}{2}

x + 2 x = \frac{5 π}{6} + 2 πn, x + 2 x = \frac{7 π}{6} + 2 πn

Solve

x + 2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{18} + \frac{2 πn}{3}

Solve

x + 2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

sec (x) - tan (x) = cos (x)

- 2 sin (x) = - sin (x) cos (x)

\frac{0.9}{cos ( x )} + (0.7 \cdot sin (x)) = 1.1

- sin^{2} (θ) + cos^{2} (θ) = 1 + sin (θ)

sin (\frac{x}{2}) = 1