Question

If tan A = 1, then find the value of 2sin Acos A.

Answer 1

Answer:

1

Step-by-step explanation:

Given,

tanA = 1

To Find :-

2sinAcosA

Solution :-

tanA = 1

we know that ,

tan45 ° = 1

Since, equating both :-

tanA = tan45 °

cancelling 'tan' on both sides :-

A = 45 °

2sinAcosA = 2sin45 °cos45 °

sin45 ° = $\sf\dfrac{1}{\sqrt{2}}$

cos45 ° = $\sf\dfrac{1}{\sqrt{2}}$

Substituting :-

= $\sf\2\times \dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}}</p><p></p><p>[tex]= 2\times \dfrac{1}{2} [since, \sqrt{2} \times \sqrt{2} = 2]$

$=\not{2}\times \dfrac{1}{\not{2}}$

= 1

Since, 2sinAcosA - 1