Question

In a right triangle ABC, right- angled at B, if tan A = 1, then verify that 2 sin A cos A =1​

Answer 1

Answer:

1

Step-by-step explanation:

In ΔABC,

⇒ tan A = (BC/AB) = 1

∴ BC = AB

Let AB = BC = k {K be some constant}

Now,

AC = √AB² + BC²

     = √k² + k²

     = √2k²

   

     = k√2

Therefore,

(i) SinA = (BC/AC)

            = k/k√2

            = 1/√2

(ii) CosA = (AB/AC)

              = k/k√2

              = 1/√2

So,

2 sinA cosA

= 2 (1/√2)(1/√2)

= 2 (1/2)

= 1

Therefore, 2 sinA cosA = 1

Hope it helps!

Answer 2

Answer:

• 2 sin A cos A = 1
• 1 = 1

Step-by-step explanation:

Given

• In a right angled Δ ABC, right angled at B,
• tan A = 1

To find

• To verify that 2 sin A cos A = 1.

Solution

In ΔABC, tan A = BC/AB = 1

BC = AB

Let AB = BC = k, where k is a positive number

• AC = √AB² + BC²
• AC = √(k)² + (k)²
• AC = k√2

(Pythagoras theorem)

Therefore,

• sin A = BC/AC = 1/√2
• cos A = AB/AC = 1/√2

Now,

• 2 sin A cos A = 1
• 2(1/√2)(1/√2) = 1
• 1 = 1
• L.H.S = R.H.S