Trigonometric Functions

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

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

Prove that:

(sin(x + y) / sin(x - y)) = (tan x + tan y) / (tan x - tan y)

Prove that:

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

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 value of

(a) sin 18°

(b) cos 18°

(c) tan 18°

(d) sin 36°

(e) cos 36°

Prove that:

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

Solve: √3 cos θ + sin θ = √2

Prove that:

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

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

Prove that:

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

Find the values of the trigonometric functions

(a) cosec (−1410°)

(b) tan (19π / 3)

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.

Show that:

tan(3x) × tan(2x) × tan(x) = tan(3x) - tan(2x) - tan(x)

Find the general solution:

sinx + sin3x+ sin5x = 0

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

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

Solve:

sin2x - sin4x + sin6x = 0