Question

if sec theta =m+n /2 root mn,find sin theta​

Answer 1

Answer:

m-n÷2√mn

Step-by-step explanation:

sec theta =m+n÷2√mn

1. according to pythagorus theorem
2. sec theta =hypotenuse ÷ adjacent
3. xsquare +4mn=msquare +nsquare +2mn
4. xsquare =msquare+n square+2 mn-4mn
5. xsquare= (m-n) whole square
6. square root on both sides
7. x=(m-n)

Answer 2

The value of $\sin \theta=\dfrac{m-n}{m+n}.$

Step-by-step explanation:

We have,

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

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

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

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

Where, h = hypotaneous, b = base

By Pyhtagoras Theorem,

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

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

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

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

= m - n

∴ $\sin \theta=\dfrac{p}{h}$

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

Thus, the value of $\sin \theta=\dfrac{m-n}{m+n}.$