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If cosx = siny and cot ( x – 40°) = tan (50° – y), then the values of x and y are :
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- x = 70°, y = 20°
- x = 75°, y = 15°
- x = 85°, y = 5°
- x = 80°, y = 10°
Correct Option: C
cosx = siny
⇒ cosx = cos (90° – y)
⇒ x = 90° – y
[∵ cos (90° – θ = sinθ)]
⇒ x + y = 90° .... (i)
Again,
cot (x – 40°) = tan (50° – y)
⇒ (cot (x – 40°) = cot {90° – (50° – y)}
[∵ cot (90° – θ) = tanθ]
⇒ x – 40° = 90° – 50° + y
⇒ x – 40 = 40 + y (i)
⇒ x – y = 40 + 40 = 80°
(ii) On adding equations (i) and (ii),
x + y + x – y = 90° + 80°
⇒ 2x = 170°
| ⇒ x = | = 85° | |
| 2 |
From equation (i),
⇒ 85° + y = 90°
⇒ y = 90° – 85° = 5°
