Q5 of 104 Page 193

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

cos θ = sin θ

⇒ tan θ = 1

now ∵ θ is an acute angle and tan θ is 1.

⇒ θ = 45

now by substituting

we get

In ΔABC, m∠B = 90, find the measure of the parts of the triangle other than the ones which are given below:

(1) m∠C = 45, AB = 5

(2) m∠A = 30, AC = 10

(3) AC = 6√2, BC = 3√6

(4) AB = 4, BC = 4

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

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

If A = 30 and B = 60, verify that

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

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