Question

If cosA=3/5, then the value of sinAtanA+1/2tan^2A is   ​

Answer 1

Given:

$\cos(a )= \frac{3}{5}$

To find:

$\sin(a) \tan(a) + \frac{1}{2} { \tan^{2} (a) }$

Solution:

Since

$\cos(a) = \frac{3}{5}$

so

$\sin(a) = \sqrt{1 - \frac{9}{25} }$

Identity used:

${ \sin^{2} (a) } + { \cos^{2} (a) } = 1$

$\sin(a) = \frac{4}{5} \\ \tan(a) = \frac{4}{3}$

Substituting the values of sin a and tan a:

$\sin(a) \tan(a) + \frac{1}{2} { \tan^{2} (a) }$

=

$( \frac{4}{5} \times \frac{4}{3} ) + \frac{1}{2} \times \frac{16}{9}$

=

$\frac{16}{15} + \frac{8}{9}$

=

$\frac{88}{45}$

Ans= 88/45