Question

If sin∅ = ⅜ then, find sec∅ + tan∅​

Answer 1

SOLUTION:-

Given:

sin theta= 3/8.

To find:

sec theta + tan theta.

Explanation:

$sin \theta = \frac{Perpendicular}{Hypotenuse} = \frac{3}{8}$

So,

Using Pythagoras Theorem:

(Hypotenuse)²=(base)²+(perpendicular)²

=) H² = B² + P²

=) 8² = B² + 3²

=) 64 = B² +9

=) B² = 64 -9

=) B² = 55

=) B=√55

Now,

$sec \theta + tan \theta \\ \\ = > \frac{H}{B} + \frac{P}{B} \\ \\ = > \frac{8}{ \sqrt{55} } + \frac{3}{ \sqrt{55} } \\ \\ = > \frac{8 + 3}{ \sqrt{55} } \\ \\ = > \frac{11}{ \sqrt{55} } \\ [Rationalise] \\ = > \frac{11 \times \sqrt{55} }{ \sqrt{55} \times \sqrt{55} } \\ \\ = > \frac{11 \sqrt{55} }{55} \\ \\ = > \frac{ \sqrt{55} }{5}$

Thank you.