1

Problem

In a right triangle ABC, right-angled at B, If tan A = 1 then find the value 2sinAcosA.

2

Step

The given value are

tan A = 1

3

Hint

If tan A = 1, it means that the length of the side opposite angle A is equal to the length of the adjacent side. Let’s denote this common length as x.

4

Formula

Since it’s a right-angled triangle, the hypotenuse can be found using the Pythagorean theorem: \$"Hypotenuse" = ("Opposite side")^2 + ("Adjacent side")^2\$

5

Step

In this case, it becomes:

\$"Hypotenuse"^2 = x^2 + x^2\$

​\$"Hypotenuse" = (2x)^2\$

\$"Hypotenuse" = x\sqrt(2)\$

6

Step

Now, substitute these values into 2sinAcosA:

\$2sinAcosA= 2 \times (x /(x \sqrt(2))) \times (x /(x\sqrt(2)))\$

7

Step

Simplify this expression:

\$2sinAcosA = 1/\sqrt2 \times 1/\sqrt2\$

\$2sinA cosA = 2/2\$

8

Step

Make it simpler:

2sinA cosA = 1

9

Solution

So, in this case, when tanA=1, the value of 2sinAcosA is 1.

10

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

11

Choice-A

This option is incorrect because it suggests a value of 2, which doesn’t match the correct calculation of 1

Wrong 2

12

Choice-B

This is the correct option as it correctly identifies the value of 2sin(A)cos(A) as 1 based on the given condition that tan(A)=1

Correct 1

13

Choice-C

This option is incorrect because it suggests a value of -1, which doesn’t match the correct calculation of 1

Wrong -1

14

Choice-D

This option is incorrect because it suggests a value of -2, which doesn’t match the correct calculation of 1

Wrong -2

15

Answer

Option

B

16

Sumup

Please summarize choices