If tan A and tan B are the roots of the equat | vedclass

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(B) Given the quadratic equation $5x^2 - 4x + 1 = 0$.Let the roots be $	an A$ and $	an B$.From the properties of quadratic equations, the sum of roo

Vedclass · Accepted Answer

$\frac{\pi}{4}$

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(B) Given the quadratic equation $5x^2 - 4x + 1 = 0$.Let the roots be $	an A$ and $	an B$.From the properties of quadratic equations, the sum of roots is $	an A + 	an B = -(\frac{-4}{5}) = \frac{4}{5}$.The product of roots is $	an A 	an B = \frac{1}{5}$.Using the trigonometric identity $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$.Substitute the values: $	an(A + B) = \frac{4/5}{1 - 1/5} = \frac{4/5}{4/5} = 1$.Since $	an(A + B) = 1$, the value of $A + B = 	an^{-1}(1) = \frac{\pi}{4}$.

If $\tan A$ and $\tan B$ are the roots of the equation $5x^2 - 4x + 1 = 0$, then the value of $A + B$ is...

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