Question

If cosx+5 sinx=3 secx then value oftanx=​

Answer 1

Step-by-step explanation:

We have,

$\cos(x) + 5 \sin(x) = 3 \sec(x)$

Dividing both sides by cos(x),

$\implies 1 + 5 \tan(x) = 3 \sec ^{2} (x)$

$\implies 1 + 5 \tan(x) = 3 (1 + \tan ^{2} (x) )$

$\implies 3\tan ^{2} (x) - 5 \tan(x) + 2 = 0$

$\implies 3\tan ^{2} (x) - 3 \tan(x) - 2 \tan(x) + 2 = 0$

$\implies 3 \tan(x)(\tan (x) - 1) - 2 (\tan(x) - 1) = 0$

$\implies( 3 \tan(x) - 2)(\tan (x) - 1) = 0$

$\implies\tan(x) = \frac{2}{3} \: or \: \tan (x) = 1$