Question

. In A ABC, B = 90° and tan A = 1. Then
prove that 2 sin A cos A = 1.​

Answer 1

Answer:

In △ABC, ∠ABC=90

o

∴tanA=

AB

BC

Since tanA=1 (Given)

AB

BC

=1 ∴BC=AB

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

Now, AC

2

=AB

2

+BC

2

∴AC=

AB

2

+BC

2

=

k

2

+k

2

∴AC=k

2

∴sinA=

AC

BC

=

k

2

k

=

2

1

,cosA=

AC

AB

=

k

2

k

=

2

1

2sinAcosA=2(

2

1

)(

2

1

)=1

∴2sinAcosA=1