2. In a AABC, if ZB = 90° and tan A = 1 then prove that 2 sin A cos A = 1..
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Answer:
Step-by-step explanation:
In △ABC, ∠ABC=90o ∴tanA=ABBC
Since tanA=1 (Given) ABBC=1 ∴BC=AB
Let AB=BC=k, where k is a positive number.
Now, AC2=AB2+BC2 ∴AC=AB2+BC2
=k2+k2
∴AC=k2
∴sinA=ACBC=k2
k=2
1,cosA=ACAB=k2
k=2
1
2sinAcosA=2(2
1)(2
1)=1
∴2sinAcosA=1
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