establish the identity Establish the identity cot 91 cot 01

establish the identity.

Establish the identity, cot 9-1 cot 0-1 ese 2e cot e Ei Consider the expression on the left side of the equality. Factor the expression in the denominator out of the numerator. Do not apply any trigonometric identity. Ask My cote 3e -1 (cot e-1)( D Print cot 0-1 cot 0-1 Enter your answer in the answer box, then click Check Answer. Mobile Apps Examples Teachers

Solution

(cot³ -1)/(cot -1)

we have a³ - b³ = (a -b)(a² + ab + b²)

==> cot³ -1³ = (cot -1) (cot² + cot (1) + 1²) = (cot -1) (cot² + cot +1)

(cot³ -1)/(cot -1) = [(cot -1) (cot² + cot +1)]/(cot -1)

==> cot² + cot +1

==> cot² +1 +cot

==> csc² +cot     since csc² -cot² = 1

Hence (cot³ -1)/(cot -1) = csc² +cot