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प्रश्न
If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ −\[\sqrt{3} \tan 3\theta\] is equal to
विकल्प
1
0
−1
\[1 + \sqrt{3}\]
उत्तर
We are given that 5θ and 4θ are acute angles satisfying the following condition sin 5θ = cos 4θ. We are asked to find 2 `sin 3θ -sqrt3 tan 3θ `
⇒ `sin 5θ= cos 4θ`
⇒` cos (90°-5θ)= cos 4θ`
⇒` 90°-5θ=4θ`
⇒ `90=90°`
Where `5θ` and `4θ` are acute angles
⇒ `θ=10°`
Now we have to find:
`2 sin 3θ-sqrt3 tan 3θ`
=` 2 sin 30°-sqrt3 tan 30°`
= `2xx1/2-sqrt3xx1/sqrt3`
=`1-1`
=` 0`
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