Question

if 4 sin alpha =5 cos alpha find the value of sec alpha tan alpha​

Answer 1

Answer:

$\frac{5 \sqrt{41} }{16}$

Step-by-step explanation:

Given,

$4 \sin \alpha = 5 \cos \alpha$

$\frac{ \sin\alpha }{ \cos\alpha } = \frac{5}{4}$

$\tan\alpha = \frac{5}{4}$

From the value of tan a, you can get sec a by using this identity

$1 + \tan^{2} \alpha = \sec^{2} \alpha$

The value of sec a will be

$\sec\alpha = \frac{ \sqrt{41} }{4}$

Hence,

$\sec\alpha \tan\alpha = \frac{ \sqrt{41} }{4} \times \frac{5}{4} = \frac{5 \sqrt{41} }{16}$