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Question
Evaluate the following without using a table:
sin 34° sec 56° + 4 cos 43° cosec 47°
Sum
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Solution
Given:
sin 34° sec 56° + 4 cos 43° cosec 47°
Step 1:
sec(90° − θ) = cosec θ
cos(90° − θ) = sin θ
sin(90° − θ) = cos θ
sec 56° = cosec(90° − 56°) = cosec 34°
cosec 47° = sec(90° − 47°) = sec 43°
Step 2:
sin 34° sec 56° ...[First term (i)]
= sin 34° ⋅ `1/(sin 34°) = 1`
4 cos 43° cosec 47° ...[Second term (ii)]
4 cos 43° ⋅ cosec 47° = 4 cos 43° ⋅ sec 43°
= 4 ⋅ cos 43° `1/(cos 43°)` = 4
= 1 + 4 ...[Adding (i) & (ii)]
= 5
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