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प्रश्न
Evaluate:
`(2 tan 30^circ sec 60^circ tan 45^circ)/(1 - sin^2 60^circ)`
मूल्यांकन
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उत्तर
Given: `(2 tan 30^circ sec 60^circ tan 45^circ)/(1 - sin^2 60^circ)`
Step-wise calculation:
1. Basic values:
`tan 30^circ = 1/sqrt(3)`
`sec 60^circ = 1/(cos 60^circ) = 1/(1/2) = 2`
tan 45° = 1
`sin 60^circ = sqrt(3)/2`
⇒ `sin^2 60^circ = 3/4`
2. Numerator:
`2 xx (1/sqrt(3)) xx 2 xx 1`
= `4/sqrt(3)`
3. Denominator:
`1 - sin^2 60^circ = 1 - 3/4`
= `1/4`
4. Division: `(4/sqrt(3)) ÷ (1/4)`
= `(4/sqrt(3)) xx 4`
= `16/sqrt(3)` Rationalized form: `(16sqrt(3))/3`
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