If A = 15°, then what is the value of 11 √(2) cos3A + 10sin2A over 7√(3) sin4A .

If A = 15°, then what is the value of 11 √(2) cos3A +…

If A = 15°, then what is the value of ${11 {\sqrt{2}} {cos3A} + 10sin2A \over 7\sqrt{3} sin4A}$ .

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 32/21

A = 15°

cos45° = 1/√2

sin30° = 1/2

sin60° = √3/2

Now, ${11 {\sqrt{2}} {cos3A} + 10sin2A \over 7\sqrt{3} sin4A}$

= (11√2 cos45° + 10sin30°)/(7√3 sin60°)

= [11√2(1/√2) + 10(1/2)]/[7√3(√3/2)]

= (11 + 5)/(21/2)

= 32/21

Therefore, the value of the given expression is 32/21.