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प्रश्न
Evaluate the following:
tan 30° cosec 60° + tan 60° sec 30°
मूल्यांकन
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उत्तर
Given: tan 30° · cosec 60° + tan 60° · sec 30°.
Step-wise calculation:
1. Use standard values:
`tan 30^circ = 1/sqrt(3)`
cosec 60° = `1/(sin 60^circ)`
= `1/(sqrt(3)/2)`
= `2/sqrt(3)`
`tan 60^circ = sqrt(3)`
`sec 30^circ = 1/(cos 30^circ)`
= `1/(sqrt(3)/2)`
= `2/sqrt(3)`
2. Compute each product:
tan 30° · cosec 60°
= `(1/sqrt(3)) · (2/sqrt(3))`
= `2/3`
tan 60° · sec 30°
= `(sqrt(3)) · (2/sqrt(3))`
= 2
3. Add:
`2/3 + 2 = 2/3 + 6/3`
= `8/3`
tan 30° · cosec 60° + tan 60° · sec 30° = `8/3`
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