Trigonometric Functions

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

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

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

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

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

Solve: √3 cos θ + sin θ = √2

Find the value of

(a) sin 18°

(b) cos 18°

(c) tan 18°

(d) sin 36°

(e) cos 36°

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

If: sinx = 3/5, cosy = −12/13, Where:x and y both lie in the second quadrant, Find the value of sin(x + y).

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

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)]

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)

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

Prove that:

cos2x × cos(x/2) − cos3x × cos × (9x/2) = sin5x × sin × (5x/2)

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

If in two circles arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii

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.