Question

24. Bandana prepared an
article on 'Save
Natural Resources', in
a right triangular board
TRY (See figure). Such
that length of TY is 1
29 cm, length of TR is -
21 cm and ZTYR = theta
Also, ZTRY = 90°. Based on the given
figure, answer the following questions :
(i) Find the value of (sin theta + cos theta )2.
(ii) Find the value of cos2 theta - sin2 theta.​

Answer 1

Answer:

1)3.9 apporx

2)0.1589 approx

Answer 2

(Sinθ + Cosθ)² = 2   & Cos²θ - Sin²θ =  -0.05

Step-by-step explanation:

TY = 29 cm

TR = 21 cm

∠TRY = 90°

RY² = TY² - TR²

=>RY² = 29² - 21²

=> RY² = (29 + 21)(29 - 21)

=> RY² = 50 * 8

=> RY² = 400

=> RY = 20

Sinθ = TR/TY  =  21/29

Cosθ = RY/TY  =  20/29

(Sinθ + Cosθ)² = (21/29 + 20/29)² = (41/29)² = 1.999 ≈ 2

Cos²θ - Sin²θ = (20/29)² - (21/29)² =  (41/29) * (-1/29) = -0.0487 ≈ -0.05

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