Question

prove that sec⁴A - sec² A= tan⁴A + tan²A​

Answer 1

Step-by-step explanation:

LHS =

${tan}^{4} a \: = {tan}^{2} \: a \\ \\ \ \\ {tan}^{2 \: } a = ( {tan}^{2} a \: + 1) \\ \\ \\ \\ {tan}^{2} a \: = ( {sec}^{2} a) \\ \\ \\ ( {sec}^{2} a \: - 1) {sec}^{2} a \\ \\ {sec}^{4} a \: = {sec}^{2} a \\ \\ = rhs \\ \\ hence \: proved....$