If $\frac{sinθ+cosθ}{sinθ-cosθ}=\frac{3}{2}$, then the value of $sin^4θ - cos^4θ$ is:

$\frac{12}{13}$

We are given that :-

\(\frac{sinθ + cosθ}{sinθ - cosθ }\) = \(\frac{3}{2 }\)

2 sinθ + 2 cosθ = 3 sinθ - 3 cosθ

 sinθ = 5 cosθ

tanθ = \(\frac{5}{1 }\)

{ we know, tanθ = \(\frac{P}{B}\) }

By using pythagoras theorem,

P² + B² = H²

5² + 1² = H²

H = √26

Now,

sin4 θ- cos4 θ

= (\(\frac{5}{√26 }\))4 - (\(\frac{1}{√26 }\) )⁴

= \(\frac{625}{676 }\) - \(\frac{1}{676 }\) 

= \(\frac{624}{676 }\)

= \(\frac{12}{13 }\)