Question

cot⁴Ɵ + cot²Ɵ = cosec⁴Ɵ – cosec²Ɵ

Answer 1

Step-by-step explanation:

as you know

${ \csc }^{2} ( \theta) = 1 + { \cot }^{2} ( \theta) \:$

squaring both side

${ (\csc ( \theta)})^{4} = (1 + {{ \cot }^{2} ( \theta) \: )}^{2} \\ = 1 + { \cot }^{4} \theta + 2 { \cot }^{2} \theta$

now

${ \csc }^{4} \theta - { \csc }^{2} \theta = \\ 1 + { \cot }^{4} \theta + 2 { \cot}^{2} \theta - 1 - { \cot }^{2} \theta \\ = { \cot}^{4} \theta + { \cot}^{2} \theta$

now I proved it hope it will help