Question

in a right angle triangle ABC right angled at B if tan A=1 then show that 2 sinA cos A=1​

Answer 1

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Answer 2

The proof is given below.

Step-by-step explanation:

In right angled triangle, right angled at B which means,

                                    ⇒ ∠B = 90⁰

Given that tan A = 1, which means that the ∠A = 45⁰.

                       ⇒ Sin A = $\frac{1}{\sqrt{2} }$ = $\frac{perpendicular}{hypotenuse}$

                   

                         ⇒ Cos A  = $\frac{1}{\sqrt{2} }$ = $\frac{xbase}{hypotenuse}$

So,

                                       ⇒ 2 Sin A Cos A = 2 x $\frac{1}{\sqrt{2} }$ x $\frac{1}{\sqrt{2} }$

which is after cancellation = 1