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

User Rozza
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Final answer:

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.

User Bennie
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