Practicing Success
The value of $\frac{1-2 \sin ^2 \theta \cos ^2 \theta}{\sin ^4 \theta+\cos ^4 \theta}-1$ is: |
-1 1 -2 sin2θ cos2θ 0 |
0 |
$\frac{1-2 \sin ^2 \theta \cos ^2 \theta}{\sin ^4 \theta+\cos ^4 \theta}-1$ = \(\frac{1 - 2 sin²θ . cos²θ}{(sin²θ)² + (cos²θ)² }\) - 1 = \(\frac{1 - 2 sin²θ . cos²θ}{(sin²θ + cos²θ)² - 2 sin²θ . cos²θ }\) - 1 { we know, sin²θ + cos²θ = 1 } - 1 = \(\frac{1 - 2 sin²θ . cos²θ}{1 - 2 sin²θ . cos²θ }\) - 1 = 0 |