If, 2 x sinq x cos(90° - q) = (1/2), such that 0° < q < 90°, then find the value of cot²2q + cos²3q.
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Correct answer: D
Explanation
Given:
2 × sinq × cos(90° − q) = 1/2
0° < q < 90°
By the formula:
cos(90° − q) = sinq
sin²q + cos²q = 1
2sinq × sinq = 1/2
2sin²q = 1/2
sin²q = 1/4
sinq = 1/2
q = 30°
2q = 60°
cot²2q = cot²60°
= (1/√3)²
= 1/3
3q = 90°
cos³3q = (cos90°)³
= 0
Therefore,
cot²2q + cos³3q = 1/3 + 0 = 1/3