## Trigonometry 7th Edition

As left side transforms into right side, hence given identity- $\frac{1 - \cos^{4} \theta}{1 + \cos^{2} \theta}$ = $\sin^{2} \theta$ is true.
Given identity is- $\frac{1 - \cos^{4} \theta}{1 + \cos^{2} \theta}$ = $\sin^{2} \theta$ Taking L.S. $\frac{1 - \cos^{4} \theta}{1 + \cos^{2} \theta}$ = $\frac{(1)^{2} - (\cos^{2} \theta)^{2}}{1 + \cos^{2} \theta}$ = $\frac{(1 + \cos^{2} \theta). (1 - \cos^{2} \theta)}{1 + \cos^{2} \theta}$ {Recall $a^{2} - b^{2}$ = (a+b)(a-b)} = $1 - \cos^{2} \theta$ = $\sin^{2}\theta$ ( Using first Pythagorean identity, $1 -\cos^{2} \theta = \sin^{2} \theta$) = R.S. As left side transforms into right side, hence given identity- $\frac{1 - \cos^{4} \theta}{1 + \cos^{2} \theta}$ = $\sin^{2} \theta$ is true.