If tan A = 1/2 and A is in the third quadrant, what is the value of sin A cos A?

Given α – β = π/4 and sin α sin β = 1/4, with α and β being acute angles, what is cos(α+β)?

Given sin α cos β = 1/5 and sin(α-β) = 1/5, what is the value of sin(α+β)?

What is the solution set for the equation cos 4x + 3 sin 2x = -1 for 0 ≤ x ≤ 180°?

What is the value of tan 105°?

Given a right triangle at Q with acute angles P and R, and sin R = 8/17, what is cos(P-R)?

What is the result of cos 7.5° cos 37.5° - sin 7.5° sin 37.5°?

Evaluate the trigonometric expression: 2 cos 23.5° cos 21.5° – 2 sin 23.5° sin 21.5°.

If cos a = 3/5 and cos b = -4/5 with a being acute and b obtuse, find cos(a+b) – cos(a-b).

What is the value of sin 75° – sin 165°?