Question

If 5sin theta - 7cos theta = 0, then find the value of sec theta.

Answer 1

$\underline\bold{\huge{ANSWER \: :}}$

5 sin theta = 7 cos theta

=> sin theta/cos theta = 7/5

=> tan theta = 7/5

So, tan theta = perpendicular/base.

Let perpendicular be 7 k units.

Similarly, let the base be 5 k units.

Hypotenuse $= \sqrt{( {7k)}^{2} + {(5k)}^{2} }$

$= \sqrt{49 \: {k}^{2} + 25 \: {k}^{2} }$

$= \sqrt{74 \: {k}^{2} }$

$= \sqrt{74} \: k$

NOW, THE VALUE OF SEC THETA

$sec \: theta \: = \: \frac{hypotenuse}{base}$

$= \frac{ \sqrt{74} k}{5k}$

$= \frac{ \sqrt{74} }{5}$