Correct Answer - Option 2 : 10
Formulas used:
sec (90 - x) = cosec x
cot (90 - x) = tan x
Calculation:
5 sin 14° sec 76° + 3 cot 15° cot 75° + 2 tan 45°
⇒ 5 sin 14° cosec 14° + cot 15° tan 15° + 2 × 1 [tan 45° = 1]
⇒ 5 sin 14° . 1/sin 14° + 3 cot 15 . 1/cot 15° + 2 [cosec x = 1/sin x]
⇒ 5 + 3 + 2 [cot x = 1/tan x]
∴ The required result = 10