Correct Answer - Option 2 : 2222/169
Given:
Sin A = 12/13.
Calculation:
In a right-angled triangle XYZ,
⇒ ∠XŶZ = 90°
⇒ sin A = XY/XZ = 12/13, cos A = YZ/XZ = ?
According to Pythagoras theorem,
⇒ XY2 + YZ2 = XZ2.
⇒ 122 + YZ2 = 132
⇒ YZ2 = 169 - 144 = 25
⇒ YZ = 5.
Now, Cos A = 5/13
According to question,
⇒ 3 Sin2 A + 4 Cos2 A + 10
⇒ 3 × (12/13)2 + 4 × (5/13)2 + 10
⇒ 3 × 144/169 + 4 × 25/169 + 10
Here, LCM of 169,1 is 169.
Now, (432 + 100 + 1690)/169
2222/169.
∴The value of 3 sin2 A + 4 cos2 A + 10 is 2222/169.