If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ − √3tan 3θ is equal to
(a)1
(b)0
(c)−1
(d)1+√3
Answers
Answered by
10
SOLUTION :
The correct option is (b) : 0
Given : sin 5θ = cos 4θ and 5θ and 4θ are acute angles.
sin 5θ = cos 4θ
cos (90° - 5θ) = cos 4θ
[cos (90° - θ) = sin θ]
On equating both sides,
(90° - 5θ) = 4θ
90° = 5θ + 4θ
90° = 9θ
θ = 90°/9
θ = 10°
The value of 2 sin 3θ - √3 tan 3θ :
= 2 sin 3 (10°) - √3 tan 3(10°)
= 2 sin 30° - √3 tan 30°
= 2 (½) - √3 (1/√3)
[sin 30° = ½ , tan 30° = 1/√3]
= 1 - 1
= 0
2 sin 3θ - √3 tan 3θ = 0
Hence, the value of 2 sin 3θ - √3 tan 3θ is 0 .
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Answered by
5
The correct option is b. 0
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