Cosx(tan x + cot x) = _____?
- Sec x
- Cos x
- Cosec x
- None of these
Explanation
Given cosx(tan x + cot x):
Step 1: Express tan x and cot x in terms of sin x and cos x
tan x = sin x / cos x
cot x = cos x / sin x
Step 2: Substitute and simplify
cosx(tan x + cot x) = cosx(sin x / cos x + cos x / sin x)
= sin x + cos² x / sin x
= (sin² x + cos² x) / sin x
= 1 / sin x (since sin² x + cos² x = 1)
Step 3: Identify the result
1 / sin x = cosec x
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