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°
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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