If sin(x)-5 cos(x)=2√6 cos(x) then the value of cot(x) is:
Given:
sin x - 5 cos x = 2 √6 cos x
Solution:
Step 1: Rearrange the equation:
sin x = 5 cos x + 2√6 cos x
sin x = (5 + 2√6) cos x
Step 2: Divide both sides by cos x to find tan x:
tan x = 5 + 2√6
Step 3: The reciprocal of tan x is 1/cot x.
Therefore:
cot x = 1/tan x
Thus, the value of cot x is 5-2√6.
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