Trigonometric Functions

Prove that:

cot(x) × cot(2x) − cot(2x) × cot(3x) − cot(3x) × cot(x) = 1

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).

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

Solve the equation:

tanx + secx =√3

Prove that: (cos x) / (1 − sin x) = tan(π/4 + x/2)

Find the value of: tan(π/8)

Find the value of

(1 + cos(π/8))(1 + cos(3π/8))(1 + cos(5π/8))(1 + cos(7π/8))

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

Find the value of tan22°30

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

Prove that:

cos(6x) = 32cos⁶(x) − 48cos⁴(x) + 18cos²(x) − 1

Solve:

2cos²x + 3sinx = 0

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

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

Draw the graph of tan x in ((-3π)/2,3π/2)