Question

In right triangle ABC, right-angled at B, if tan A = √3, then the value of

2sin A cos C is

1. √3 /2
2. 0
3. 1/√3 
4. 3/2

Answer 1

Correct Answer - Option 4 : 3/2

Formula used:

In a Δ ABC,

∠A +  ∠B +  ∠C = 180∘

Calculation:

Given that,

∠B = 90^∘ 

tan A = √3

⇒ tan A = tan 60^∘ 

⇒ ∠A = 60^∘ 

∵ ∠A +  ∠B +  ∠C = 180^∘

⇒  60^∘ + 90^∘  + ∠C = 180∘

⇒ ∠C = 30∘

Hence, the required value

2sin A cos C = 2 sin 60∘cos 30∘

= 2 × (√ 3/2) × (√3/2)

⇒ 2sin A cos C = 3/2