Question

prove that cosec^2θ-cos^2θ/cot^2θ=sec^2θ-sin^2θ​

Answer 1

Answer:

Step-by-step explanation:

$\frac{ cosec^{2}x - cos^{2}x}{{cot^{2}x}}\\=\frac{\frac{1}{sin^{2}x} - cos^{2}x}{\frac{cos^{2}x}{sin^{2}x}}\\=({\frac{1}{sin^{2}x} - cos^{2}x})(\frac{sin^{2}x}{cos^{2}x})\\=({\frac{1 - cos^{2}xsin^{2}x}{sin^{2}x})(\frac{sin^{2}x}{cos^{2}x})\\=({\frac{1 - cos^{2}xsin^{2}x}{cos^{2}x})\\=\frac{1}{cos^{2}x} - \frac{cos^{2}xsin^{2}x}{cos^{2}x}\\=sec^{2}x - sin^{2}x$