Question

In aright angle triangle ABC,right angled tab if tan A= 1 then show that 2sin A cosA=1

Answer 1

Answer:

2sinAcosA = 1.

Step-by-step explanation:

= > tanA = 1

= > tanA = tan45°

= > A = 45°

= > 2A = 90°

= > sin( 2A ) = sin90°

= > sin2A = 1

From the trigonometric properties :

• sin2B = 2sinBcosB

Thus,

= > sin2A = 1

= > 2sinAcosA = 1

Hence proved.

Answer 2

Question :-- In aright angle triangle ABC,right angled at B if tan A= 1 then show that 2sin A cosA=1 ?

Formula used :--

→ tan45° = 1

→ 2sinA*cosA = Sin2A .

→ Sin90° = 1

Solution :--

given, tan A = 1 ,

putting 1 = tan45° we get ,

→ tanA = tan45°

comparing now we get,

→ A = 45° ---------- Equation (1)

Now, we have to find , 2SinA*cosA = ?

→ 2SinA*cosA = sin2A

Putting value of A From Equation (1) we get,

→ Sin2A = Sin(2*45°)

→ Sin2A = Sin90°

→ Sin2A = 1

✪✪ Hence Proved ✪✪

So,

2sinA * cosA=1