In a right triangle ABC, right angled at B, if tanA = 1, then verify that 2sinA cosA = 1
Answers
Answered by
1
Step-by-step explanation:
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
Attachments:
Similar questions