Question

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

Answer 1

Answer:

Step-by-step explanation:In △ABC, ∠ABC=90o

∴tanA= AB BC

Since tanA=1 (Given)  

AB BC =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=AC BC =k2 K =2 1 ,cosA=AC AB =k2 k =2 1 2sinAcosA=2(2 1 )(2 1 )=1 ∴2sinAcosA=1