Question

2)If triangle RPQ is a right angled triangle at Q. If PQ = 5cm and RQ = 10 cm,find (i) sin ^2 P (ii) cos ^2 R and tan R (iii) sin P X cos P (iV) sin ^2 P –cos ^2p

Answer 1

Answer: (i) 1 (ii) 3/4 , √3/3 (iii) 0 (iv) 1

Explanation:

ΔRPQ is 1 30°-60°-90° triangle because RQ = 2PQ , where

• ∠R = 30°
• ∠P = 90°
• ∠Q = 60°

(i) sin² (90°) = 1² = 1

`\text{(ii)}\ \cos ^2(30^o)= \bigg((\sqrt3)/(2)\bigg)^2=(3)/(4)`

`.\quad \tan (30^o)=(1)/(\sqrt3)\bigg=(\sqrt3)/(3)`

(iii) sin (90°) × cos (90°) = 1 × 0 = 0

(iv) sin² (90°) - cos² (90°) = 1² - 0² = 1