Question

Read the following question carefully and answer the questions that follow.
27. Prove that:
please answer me as soon as possible​

Answer 1

Step-by-step explanation:

$2 {sec}^{2} \theta - {sec}^{4} \theta - 2 {cosec}^{2} \theta + {cosec}^{4} \theta \\ \\= {cot}^{4} \theta - {tan}^{4} \theta \\\\ LHS \\\\= 2 {sec}^{2} \theta - {sec}^{4} \theta - 2 {cosec}^{2} \theta + {cosec}^{4} \theta \\\\ = 2 {sec}^{2} \theta - ({sec}^{2})^{2} \theta - 2 {cosec}^{2} \theta + ({cosec}^{2} )^{2} \theta \\\\ = 2(1 + {tan}^{2} \theta) - (1 + {tan}^{2} \theta)^{2} \\\\ - 2(1 + {cot}^{2} \theta) + (1 + {cot}^{2} \theta)^{2} \\ \\= 2 + 2{tan}^{2} \theta - 1 - {tan}^{4} \theta - 2{tan}^{2} \theta \\\\ - 2 - 2 {cot}^{2} \theta + 1 + {cot}^{4} \theta + 2 {cot}^{2} \theta \\\\ = {cot}^{4} \theta - {tan}^{4} \theta \\\\ = RHS \\\\ Hence \: Proved$