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If cos x = sin y and cot (x - ­35°) = tan (35°­ - y), then the value of x and y are

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If cos x = sin y and cot (x - ­35°) = tan (35°­ - y), then the value of x and y are
1). x = 90°, y = 0°
2). x = 75°, y = 15°
3). x = 85°, y = 5°
4). x = 80°, y = 10°


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Answered by on | Votes 1 |

cos x = sin y

⇒ cos x = cos(90° – y)

⇒ x = 90° – y

⇒ x + y = 90°        ….(1)

cot (x­ - 35°) = tan (35°­ - y)

⇒ cot (x – 35°) = cot (90° – (35° - y))

⇒ x – 35° = 55° + y

⇒ x – y = 90°        ….(2)

Solving (1) and (2)

We get,

x = 90° and y = 0°

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