Question

If sin theta is equal to 24/25 find tan theta+sec theta

Answer 1

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Answer 2

Answer:

$tan{\theta}+sec{\theta}=7$.

Step-by-step explanation:

It is given that the value of $sin{\theta}$ is ${\frac{24}{25}}$, that is

$sin{\theta}=\frac{perpendicular}{Hypotenuse}=\frac{24}{25}$

Now, using the Pythagoras theorem, we have

$(25)^2=(24)^2+(Base)^2$

$625-576=(Base)^2$

$49=(Base)^2$

$7=Base$

Now, $tan{\theta}={\frac{Perpendicular}{Base}=\frac{24}{7}$

And $sec{\theta}=\frac{Hypotenuse}{Base}=\frac{25}{7}$

thus, the value of $tan{\theta}+sec{\theta}$ will be:

$tan{\theta}+sec{\theta}=\frac{24}{7}+\frac{25}{7}$

$tan{\theta}+sec{\theta}=\frac{49}{7}$

$tan{\theta}+sec{\theta}=7$.