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Question
Find the value of:
tan2 60° cosec2 45° + sec2 60° sin 30°
Sum
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Solution
Given:
tan2 60° cosec2 45° + sec2 60° sin 30°
Step 1: Recall standard values
tan 60° = `sqrt3 → tan^2 60° = 3`
cosec 45° = `1/(sin 45°) = sqrt2 → "cosec"^2 45° = 2`
`sec 60° = 1/(cos 60°) = 2 → sec^2 60° = 4`
sin 30° = `1/2`
Step 2: Calculate each part
tan2 60° ⋅ cosec2 45° = 3 ⋅ 2 = 6
sec2 60° ⋅ sin 30° = 4 ⋅ `1/2` = 2
= 6 + 2 ...[Adding]
= 8
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