Trigonometric Functions

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

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

Prove that: sin10° sin30° sin50° sin70° = ¹/₁₆

cosA × cos2A × cos4A × cos8A = ^{sin 16A}/_{16 sin A}

Find the values of other five trigonometric functions is

(a) cot x = 3/4, x lies in third quadrant.

(b) sec x = 13/5, x lies in fourth quadrant.

Prove that:

(sin(5x) - 2·sin(3x) + sin(x)) / (cos(5x) - cos(x)) = tan(x)

Solve: √3 cos θ + sin θ = √2

Prove that: cos²A + cos²B - 2 cos A cos B cos(A + B) = sin²(A + B)

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

Prove that:

sin²(6x) − sin²(4x) = sin(2x) × sin(10x)

If tan A = ⁵/₆, tan B = ¹/₁₁, prove that A + B = π/4.

Prove that:

(tan(x/4 + x)) / (tan(x/4 - x)) = ((1 + tan(x)) / (1 - tan(x)))²

Prove that:

tan(4x) = [4tan(x) × (1 − tan²(x))] / [1 − 6tan²(x) + tan⁴(x)]

Prove: (cos 11° + sin 11°) / (cos 11° - sin 11°) = tan 56°

Solve:

sin2x - sin4x + sin6x = 0

Find the values of other five trigonometric functions is

(a) cot x = 3/4, x lies in third quadrant.

(b) sec x = 13/5, x lies in fourth quadrant.

Find the values of the trigonometric functions

(a) cosec (−1410°)

(b) tan (19π / 3)

If tan α = m / (m + 1), tan β = 1 / (2m + 1), then find the value of α + β.

Find the value of

(a) sin 18°

(b) cos 18°

(c) tan 18°

(d) sin 36°

(e) cos 36°