Trigonometric Functions

Find sin(x/2), cos(x/2) and tan(x/2), if tan(x) = −4/3, x in quadrant II

asin(B − C) + bsin(C − A) + csin(A − B) = 0

asin(B − C) + bsin(C − A) + csin(A − B) = 0

Prove that: cos²x + cos²(x + π/3) + cos²(x − π/3) = 3/2

Solve:

2cos²x + 3sinx = 0

Prove that: tanα tan(60° - α) tan(60° + α) = tan3α

Show that: √(2 + √(2 + 2cos 4θ)) = 2cos θ

Prove: (tan 5θ + tan 3θ) / (tan 5θ − tan 3θ) = 4 cos 2θ · cos 4θ

(sin(B − C)) / (sin(B + C)) = (b² − c²) / a²

(a² + b²) / (a² + c²) = [(1 + cos(A − B)) × cos(C)] / [(1 + cos(A − C)) × cos(B)]

Prove: sin 20° × sin 40° × sin 60° × sin 80° = 3/16

a cosA + b cosB + c cosC = 2a sinB sinC

If α and β are the solutions of the equation a tan θ + b sec θ = c, then show that tan(α + β) = (2ac) / (a² − c²).

If α and β are the solutions of the equation a tan θ + b sec θ = c, then show that tan(α + β) = (2ac) / (a² − c²).

Prove that: (sec8θ − 1) / (sec4θ − 1) = tan8θ / tan2θ