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Finding the unknown angle from the given trigonometric expressions
1) If sin (x + y) = 1 and cos (x - y) = √3/2, find x and y.
40, 50
60, 30
45, 45
50, 40
1/10
Solution
Answer:
60, 30
Explanation:
sin (x + y) = 1
sin (x + y) = sin 90°, [since sin 90° = 1]
= x + y = 90°
cos (x - y) = √3/2
cos (x - y) = cos 30°
x - y = 30°
x + y = 90° ------- (A)
2x = 120°
x = 60°,
Putting the value of x = 60° in (A) we get,
60° + y = 90°
Subtract 60° from both sides
60° + y = 90°
y = 30°
Therefore, x = 60° and y = 30°
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