(tanx + cotx)2 − (tanx − cotx)2

is gelijk aan
A.   1
B.   2
C.   0
D.   4
E.   2 cot2 x
                 

[ 4-4764 - op net sinds 29.10.12-(E)-27.10.2023 ]

Translation in   E N G L I S H

(tanx + cotx)2 − (tanx − cotx)2

is equal to
A.   1
B.   2
C.   0
D.   4
E.   2 cot2 x

Oplossing - Solution

1ste manier :
(tan x + cot x)² − (tan x − cot x)²
= tan²x + 2.tan x.cot x + cot²x − (tan x − 2.tan x.cot x + cot² x)
= tan² x + 2 + cot² x − (tan² x − 2 + cot² x)
= tan² x + 2 + cot² x − tan² x + 2 − cot² x = ...
2de manier :
(tan x + cot x)² − (tan x − cot x)²
= (tan x + cot x + tan x − cot x)(tan x + cot x − tan x + cot x)
= 2.tan x.2.cot x = ...