Question

if 7sin^2a+3 cos^2a=4 find the value of √3tanA

Answer 1

In the attachment I have answered this problem.

The given equation is modified in such a way that it completely contains tan squares.

See the attachment for detailed solution

Answer 2

Hey there!

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Here's your solution :

$7 sin^{2} A + 3 cos^{2} = 4$

⇒ $4sin^{2} A + 3 sin^{2} A + 3 cos^{2} A = 4$

⇒ $4 sin^{2} A + 3(sin^{2} A + cos^{2} A) = 4$

⇒ $4 sin^{2} A + 3 × 1 = 4$ $[ ∵ sin^{2} A + cos^{2} A = 1]$

⇒ $4sin^{2} A = 1$ ⇒ $sin^{2} A = \frac{1}{4}$

∴ $cos^{2} A = (1 - sin^{2} A) = ( 1 - \frac{1}{4} ) = \frac{3}{4}$

∴ $tan^{2} A = \frac{sin^{2} A}{cos^{2} A} = (\frac{1}{4} \times \frac{4}{3}) = \frac{1}{3}$

Hence, tan A = $\pm \frac{1}{\sqrt{3}}$

Now, taking $\sqrt{3}$ from RHS to LHS.

Therefore, $\sqrt{3} tan A = 1$