Question

solve the following​

Answer 1

Step-by-step explanation:

${sec}^{4} A(1 - {sin}^{4} A) - 2 {tan}^{2} A = 1 \\ LHS = {sec}^{4} A(1 - {sin}^{4} A) - 2 {tan}^{2} A \\ = {sec}^{4} A(1 - {sin}^{2} A)(1 + {sin}^{2} A) - 2 {tan}^{2} A \\ = {sec}^{2} A \times {sec}^{2} A \times {cos}^{2}A(1 + {sin}^{2} A) - 2 {tan}^{2} A \\ = {sec}^{2} A (1 + {sin}^{2} A) - 2 {tan}^{2} A \\ = {sec}^{2} A + {sec}^{2} A {sin}^{2} A - 2 {tan}^{2} A \\ =1 + {tan}^{2} A + \frac{1}{ {cos}^{2} A} {sin}^{2} A - 2 {tan}^{2} A \\ =1 + {tan}^{2} A + \frac{{sin}^{2} A}{ {cos}^{2} A} - 2 {tan}^{2} A \\ =1 + {tan}^{2} A + {tan}^{2} A - 2 {tan}^{2} A \\ = 1 + 2 {tan}^{2} - 2 {tan}^{2} \\ = 1 \\ = RHS \\ Thus \: Proved$

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