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Find the value of 5 sin 15° sec 75° + 2 tan 45° + 3 sec30°.
1. 9
2. 10
3. 11
4. 12
5. 13

1 Answer

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Correct Answer - Option 3 : 11

Given:

5 sin 15° sec 75° + 2 tan 45° + 3 sec30°

Calculation:

5 sin 15° sec 75° + 2 tan 45° + 3 sec30°

⇒ 5 sin 15° sec(90° - 15°) + 2 tan 45° + 3 sec30°

⇒ 5 sin 15° cosec 15° + 2 tan 45° + 3 sec30°

⇒ 5 sin 15°(1/sin 15°) + 2 × 1 + 3 (2/√3)2

⇒ 5 + 2 + 4

⇒ 11

∴ The value of 5 sin 15° sec 75° + 2 tan 45° + 3 sec30° is 11.

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