सिद्ध कीजिए कि : ` sec^(4) theta - tan ^(4) theta = 1 + 2 tan^(2) theta `

Explanation

L.H.S. = ` sec^(4) theta - tan^(4) theta = (sec^(2) theta )^(2) - (tan^(2) theta)^(2)`
` = (sec^(2) theta + tan^(2) theta ) (sec^(2) theta - tan^(2) theta ) = (1 + tan^(2) theta + tan^(2)theta) (1+ tan^(2) theta+ tan^(2) theta )(1 + tan^(2) theta - tan^(2) theta)`
` (1 + 2 tan^(2) theta ) (1) = 1 + 2 tan^(2) theta ` = R.H.S