Question

tan theta + sec theta is equal to 1.5 find the value of sin theta, tan theta ,sec theta .​

Answer 1

Refer The attachment ⬆

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Answer 2

Answer:

$Sin \theta = \frac{Perpendicular}{Hypotenuse}=\frac{5}{13}\\Sin \theta = \frac{Perpendicular}{Base}=\frac{5}{12}\\Sec \theta = \frac{Hypotenuse}{Base}=\frac{13}{12}$

Step-by-step explanation:

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

To Find : sin theta, tan theta ,sec theta .​

Solution :

$tan\theta +sec\theta = 1.5$

$tan\theta +\sqrt{1+Tan^2 \theta} = 1.5$

$\sqrt{1+Tan^2 \theta} = 1.5-tan \theta$

$1+Tan^2 \theta= (1.5-tan \theta)^2$

$1+Tan^2 \theta=\frac{9}{4}+Tan^2\theta - 3 tan \theta$

$1-\frac{9}{4}= - 3 tan \theta$

$-\frac{5}{4}= - 3 tan \theta$

$\frac{5}{4}= 3 tan \theta$

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

$Tan \theta = \frac{Perpendicular}{Base}$

On comparing Perpendicular = 5

Base = 12

$Hypotenuse^2=Perpendicular^2+base^2$

$Hypotenuse^2=5^2+12^2$

$Hypotenuse=\sqrt{5^2+12^2}$

$Hypotenuse=13$

$Sin \theta = \frac{Perpendicular}{Hypotenuse}=\frac{5}{13}\\Sin \theta = \frac{Perpendicular}{Base}=\frac{5}{12}\\Sec \theta = \frac{Hypotenuse}{Base}=\frac{13}{12}$