Question

In a triangle ABC, right-angled at C, in which AB = 29 units, BC = 21 units and ∠ABC = Ө. Determine the values of

(a)Cos2Ө + sin2Ө

(b)Cos2Ө – sin2Ө

Answer 1

Answer:

1, 41/841

Step-by-step explanation:

Given, AB = 29 units, BC = 21 units, ∠ABC = Ф.

By Pythagoras theorem, we get

⇒ AB² = AC² + BC²

⇒ AC² = AB² - BC²

           = (29)² - (21)²

           = 400

AC = 20 units.

∴ cosФ = BC/AB

            = 21/29.

∴ sinФ = AC/AB

           = 20/29

(i) cos²Ф + sin²Ф

= (21/29)² + (20/29)²

= (441 + 400)/841

= 1

(ii) cos²Ф - sin²Ф

= (21/29)² - (20/29)²

= (441 - 400)/841

= (41/841)

Hope it helps!

Answer 2

hope this answer will help you.