Question

If tan thita + sec thita =1.5 .Then find value of sin thita?

Answer 1

Answer:

$\tan \theta + \sec \theta \: = 1.5$

$2 \tan \theta \: + 2 \sec \theta \: = 3$

$2 \sec \theta \: = 3 - 2 \tan \theta$

${4 \sec }^{2} \theta \: = {(3 - 2 \tan \theta)}^{2}$

$4 + 4 { \tan }^{2} \theta = 9 - 12 \tan \theta + 4 { \tan }^{2} \theta$

$\tan \theta \: = \frac{5}{12}$

and

$\sin \theta \: = \frac{5}{13}$

then

$\frac{ \sin \theta }{ \cos \theta } + \frac{1}{ \cos \theta } = \frac{3}{2}$

$2 \sin \theta \: + 2 = 3 \cos \theta$

${(2 \sin \theta + 2) }^{2} = 9 { \cos }^{2} \theta$

$13 { \sin }^{2} \theta + 8 \sin \theta - 5$

=0

$\sin \theta \: = \frac{5}{13}$

this is your answer