Correct Answer - Option 2 : 2222/169

**Given:**

SinA = 12/13.

**Calculation:**

In a right-angled triangle XYZ,

⇒ ∠XŶZ = 90°

⇒ sinA = XY/XZ = 12/13, cosA = YZ/XZ = ?

According to Pythagoras theorem,

⇒ XY^{2} + YZ^{2 }= XZ^{2.}

⇒ 12^{2} + YZ^{2} = 13^{2}

⇒ YZ^{2} = 169 - 144 = 25

⇒ YZ = 5.

Now, CosA = 5/13

According to question,

⇒ 3Sin^{2}A + 4Cos^{2}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.

**∴T****he value of 3sin**^{2}A + 4cos^{2}A + 10 is 2222/169.