If α is measure of acute angle and 3sinα = 2cosα, prove that

In a rectangle ABCD, AB = 20, m∠BAC = 60, calculate the length of side and diagonals and.

If θ is measure of an acute angle and cosθ = sinθ, find the value of 2tan²θ + sin²θ + 1.

If A = 30 and B = 60, verify that

sin(A + B) = sinA cosB + cosA sinB,

If A = 30 and B = 60, verify that

cos(A + B) = cosA cosB – sinA sinB