Question : If $5 \sin^2 A+3 \cos^2 A=4$, $0<A<90°$, then what is the value of $\tan A$?
Option 1: 0
Option 2: 3
Option 3: 1
Option 4: 2
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Correct Answer: 1
Solution :
Given: $5\sin^2 A+3\cos^2 A=4$
⇒ $2\sin^2 A+ 3\sin^2A + 3\cos^2 A=4$
⇒ $2 \sin^2 A+3=4$...........[Using $ \sin^2 A+ \cos^2 A=1$]
⇒ $\sin^2 A=\frac{1}{2}$
⇒ $\sin A=\frac{1}{\sqrt{2}}$
⇒ $A=45°$
So, $\tan A=1$
Hence, the correct answer is 1.
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