1.

In right angle triangle at B, if tan A=1,then verify that 2 sin A cos A=1.​

Answer»

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


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