Question

if sec theta is equals to M + n bi to root m n find sin theta​

Answer 1

$\sin \theta$ $=\dfrac{m-n}{m+n}}$

Step-by-step explanation:

We have,

$\sec \theta=\dfrac{m+n}{2\sqrt{mn}}$

To find, the value of $\sin \theta$ =?

∴ $\sec \theta=\dfrac{m+n}{2\sqrt{mn}}$

We know that,

The trigonometric identity,

$\sec \theta=\dfrac{h}{b}$

∴ Base (b) = $2\sqrt{mn$ and hypotaneous (h) = m + n

By Pythagoras theorem,

Perpendicular, $p=\sqrt{h^{2}-b^{2}}$

p=$\sqrt{(m + n)^{2}-(2\sqrt{mn})^{2}}$

= $\sqrt{(m + n)^{2}-4mn}$

= $\sqrt{(m - n)^{2}}$

= m - n

Using the algebraic identity,

$(a-b)^{2}=(a+b)^{2}-4ab$

Perpendicular, p = m - n

∴ $\sin \theta=\dfrac{p}{h}$

$=\dfrac{m-n}{m+n}}$

Thus, $\sin \theta$ $=\dfrac{m-n}{m+n}}$