Question

pls answer this question......​

Answer 1

Step-by-step explanation:

${cot}^{4} \theta \: - 1 = {cosec}^{4} \theta \: -2 {cosec}^{2} \theta \\ LHS = {cot}^{4} \theta \: - 1 \\ = ( {cot}^{2} \theta)^{2} \: -( 1)^{2} \\ = ( {cot}^{2} \theta \: + 1)( {cot}^{2} \theta \: - 1) \\ = {cosec}^{2} \theta( {cot}^{2} \theta \: - 1) \\ = {cosec}^{2} \theta( \{ {cosec}^{2} \theta - 1 \} \: - 1) \\ = {cosec}^{2} \theta( {cosec}^{2} \theta - 1 - 1) \\ = {cosec}^{2} \theta( {cosec}^{2} \theta - 2) \\ = {cosec}^{2} \theta \times {cosec}^{2} \theta - 2 \times {cosec}^{2} \theta \\ = {cosec}^{4} \theta - 2 {cosec}^{2} \theta \\ </strong><strong>=</strong><strong> </strong><strong>RHS \\ thus \: proved$