Question

If Cot A = 12/5, then the value of (Sin A + Cos A) × Cosec A is
1. 17/5
2. 13/5
3. 14/5
4. 1

Answer 1

Correct Answer - Option 1 : 17/5

Given ;

cot A =12/5 = B/P

B = 12  and  P = 5

Formula used ; 

H² = B² + P²

Calculation; 

⇒ H = √(B² + P²)

⇒ H = √(12² + 5²)

⇒ H = √(144 + 25)

⇒ H = √169

⇒ H = 13 

then sin A = P/H 

⇒ sin A = 5/13 

cos A = B/H   

⇒ cos A = 12/13 

cosec A = H/P 

⇒ cosec A = 13/5

⇒ (sin A + cos A ) × cosec A = (5/3 +12/13) × 13/5 

⇒ 17/13 × 13/5 = 17/5 

∴  The required answer is  17/5