Question

If 1 + sin2A = 3sinA cosA, then sum of all possible value of tanA is:______

Answer 1

To find the sum of all possible values of tanA, given 1 + sin²A = 3sinA cosA, we must solve the quadratic equation 1 = tanA(3 - tan²A).

Step-by-step explanation:

The student is asked: If 1 + sin²A = 3sinA cosA, then sum of all possible values of tanA is:______. This is a Mathematics problem related to trigonometric identities. Let's first rearrange the equation to express everything in terms of sine and cosine:

1 + sin²A = 3sinA cosA

Now, recall that tanA is the ratio of sinA to cosA (tanA = sinA/cosA). To find the sum of all possible values of tanA, we need to find the values of A for which the above equation holds true.

Rewrite the equation as:

1 = 3sinA cosA - sin²A

1 = sinA(3cosA - sinA)

Because 1 = cos²A + sin²A, rewrite the equation again as:

cos²A = sinA(3cosA - sinA)

Divide both sides by cos²A to get:

1 = tanA(3 - tan²A)

This quadratic equation can now be solved for tanA. Once we have the values of tanA, we can add them to find the sum of all possible values of tanA.