establish the identity Establish the identity sec 0 tan 0 se

establish the identity.

Establish the identity. sec 0+ tan 0 sec 0+ tan 0 cos 0 cot 0 sec 0 tan 0 subtract the fractions on the left side. Apply the appropriate Pythagorean identity to simplif the numerator. (Simplify your answer.) sec 0 tan 0

Solution

{(sec theta + tan theta ) / tan theta} - {(sec theta + tan theta ) / sec theta} = cos theta cot theta

taking common denominator as sec theta tan theta

(sec^2 theta + tan theta sec theta - sec theta tan theta - tan^2 theta ) / (sec theta tan theta )

= sec^2 theta - tan^2 theta / (sec theta tan theta )

sec^2 theta - tan^2 theta = 1

so we get

1 / (sec theta tan theta ) = cos theta cot theta

numerator will be 1