Question

find the value of other trigonometric ratios given that sin theta is equal to m square minus n square upon m square + n square

ie sin o = m^2-n^2/m^2+n^2​

Answer 1

$\huge\bf\underbrace{☆ANSWER☆}$

Solution:

$⇒sinФ=(m²-n²)/(m²+n²)$

Since sinФ=Perpendicular/Hypotenuse

$→H²=B²+P²$

$→(m²+n²)²=B²+(m²-n²)$

$→B²=(m²+n²)-(m²-n²)²$

$→B²=(m²+n²+m²-n²)(m²+n²-m²+n²)$

$→B=√(2m²ˣ2n²)$

$→B=2mn$

$*cosФ=B/H$

$*secФ=H/B$

$*cosecФ=H/P$

$*tanФ=P/B$

$*cotФ=B/P$

$⇒cosФ=2mn/(m²+n²)$

$⇒secФ=(m²+n²)/2mn$

$⇒cosecФ=(m²+n²)/2mn$

$⇒tanФ=(m²-n²)/2mn$

$⇒cotФ=2mn/(m²-n²)$