Question

If SinA = 12/13, then find the value of 3Sin²A + 4Cos²A + 10

1. 13/169
2. 2222/169
3. 222/169
4. 13

Answer 1

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,

⇒ XY² + YZ² = XZ^2.

⇒ 12² + YZ² = 13²

⇒ YZ² = 169 - 144 = 25

⇒ YZ = 5.

Now, CosA = 5/13

According to question,

⇒ 3Sin²A + 4Cos²A + 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 3sin²A + 4cos²A + 10 is 2222/169.