Trigonometric Functions

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

Find the general solution:

sinx + sin3x+ sin5x = 0

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

Prove that:

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

Prove that: tan 36° + tan 9° + tan 36° tan 9° = 1

Find the value of

(a) sin 18°

(b) cos 18°

(c) tan 18°

(d) sin 36°

(e) cos 36°

Find the value of: tan(π/8)

Solve: 2tan²x + sec²x = 2, for 0 ≤ x ≤ 2π

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

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

Prove that: (tan(A + B)) / (cot(A - B)) = (tan²A - tan²B) / (1 - tan²A × tan²B)

Find the value of: tan(π/8)

Prove: cos(π/5) × cos(2π/5) × cos(4π/5) × cos(8π/5) = −1/16

If: tanx = 3/4, π < x < 3π/2, find the value of: sin(x/2), cos(x/2), tan(x/2)

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

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

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

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

In triangle ABC, prove that:

tan((B − C)/2) = (b − c)/(b + c) × cot(A/2)

tan((C − A)/2) = (c − a)/(c + a) × cot(B/2)

tan((A − B)/2) = (a − b)/(a + b) × cot(C/2)

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