হলে, Θ এর মান কত? যেখানে Θ সুক্ষ্মকোণ?
Created: 1 year ago |
Updated: 2 months ago
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2 sin 2 Θ + 3cos Θ - 3 = 0
2(1 – cos2 Θ) +3cos Θ-3 = 0
2 – 2cos2 Θ +3 cos Θ -3 =
-2cos2 Θ+3cos Θ = 1
3cos Θ-2cos2 Θ=1
2cos Θ(1-cos Θ) = 1
| 2cos Θ = 1 Cos Θ = ½ cos Θ = cos60 | And 1-cos Θ = 1 cos Θ = 0 cos Θ = cos 90 |
So, 60<Θ<90
Answer, 60
Option test:
L.H.S
2×(sin60°)2 + 3cos60° - 3
= 2 × (√3/2)2 + 3 ×(½) -3
= 2 × (¾) + 3/2 -3
= 3 - 3
= 0
=R.H.S
2 sin 2 Θ + 3cos Θ - 3 = 0
2(1 – cos2 Θ) +3cos Θ-3 = 0
2 – 2cos2 Θ +3 cos Θ -3 = 0
-2cos2 Θ + 3cos Θ - 1 = 0
2cos2 Θ - 3cos Θ + 1 = 0
2cos2 Θ - 2cos Θ - cos Θ + 1 = 0
2cos Θ(cos Θ-1) -1(cos Θ-1) = 0
(cos Θ-1)(2cos Θ-1) = 0
| (2cos Θ-1) = 0 2cos Θ = 1 Cos Θ = ½ cos Θ = cos60 Θ = 60 | And (cos Θ -1) = 0 cos Θ = 1 cos Θ = cos 0 Θ = 0 |
Thus Θ = 0 and 60.
Answer is 0 and 60
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