Question

please do this and get 10 points

Answer 1

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: prove : \\ 2sec {}^{2} x - sec {}^{4} x - 2.cosec {}^{2} x + cosec {}^{4} x = \\ \frac{1 - tan {}^{8} \: x}{tan {}^{4} \: x } \\ \\ LHS = 2sec {}^{2} x - sec {}^{4} x - 2cosec {}^{2} x + cosec {}^{4} x \\ \\ = 2(1 + tan {}^{2} x) - (1 + tan {}^{2} x) {}^{2} - \\ 2(1 + cot {}^{2} x) + (1 + cot {}^{2} x) {}^{2} \\ \\ = 2 + 2tan {}^{2} x - 1 - tan {}^{4} x - 2tan {}^{2} x \\ - 2 - 2cot {}^{2} x + 1 + cot {}^{4} x + 2cot {}^{2} x \\ \\ = cot {}^{4} x - tan {}^{4} x \\ \\ = \frac{1}{tan {}^{4} x} - tan { }^{4} x \\ \\ = \frac{1 - tan {}^{8}x }{tan {}^{4}x } \\ \\ = RHS$