Q12 of 104 Page 188

In ΔABC, m∠B = 90, AC + BC = 25 and AB = 5, determine the value of sinA, cosA and tanA.

AC = 25 – BC

AC² = AB² + BC² (by Pythagoras theorem)

(25–BC)² = (5)² + BC²

⇒ BC = 12

⇒ AC = 13 (by AC = 25 – BC)

By Pythagoras theorem

(25–BC)² = 5² + BC²

⇒ BC = 12

⇒ AC = 13 and AB = 5

we know that

⇒

If tanA = √3, verify that

(1) sin²A + cos²A = 1

(2) sec²A – tan²A = 1

(3) 1 + cot²A = cosec²A

If cos θ = , verify that tan²θ – sin²θ = tan²θ⋅ sin²θ

In ΔABC, m∠C = 90 and m∠A = m∠B,

(1) Is cosA = cosB?

(2) Is tanA = tanB?

(3) Will the other trigonometric ratios of ∠A and ∠B be equal?

If 3cotA = 4, examine whether cos²A – sin²A.