In a right ∆ABC , right-angled at B, if tan A = 1 , then verify that

1.	In a right ∆ABC , right-angled at B, if tan A = 1 , then verify that 2 sin A·cos A = 1.
Answer» Consider ΔABC to be a right angled triangle at B. angle C = 90 degree Given: tan A = 1 …(1) tan A = 1 = BC/AB AB = BC Again, tan A = sin A/cos A sin A = cos A …using (1) By Pythagoras theorem: AC² = BC² + AB² AC² = 2BC² (AC/BC)² = 2 Or AC/BC = √2 cosec A = √2 or sin A = 1/√2 and cos A = 1/√2 Now, 2 sin A cos A = 2(1/√2)( 1/√2) = 2(1/2) = 1 = RHS

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

Answer»

Consider ΔABC to be a right angled triangle at B.

angle C = 90 degree

Given: tan A = 1 …(1)

tan A = 1 = BC/AB

AB = BC

Again, tan A = sin A/cos A

sin A = cos A …using (1)

By Pythagoras theorem:

AC² = BC² + AB²

AC² = 2BC²

(AC/BC)² = 2

Or AC/BC = √2

cosec A = √2

or sin A = 1/√2

and cos A = 1/√2

Now,

2 sin A cos A = 2(1/√2)( 1/√2)

= 2(1/2)

= 1

= RHS