Prove that tan x + cot X can never be equal to 3/2
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Step-by-step explanation:
Say, y=tanx + cotx
y=(sinx/cosx)+(cosx/sinx)
y=[(sin²x+cos²x)/(sinxcosx)]
Sin²x+cos²x=1
y=1/(sinxcosx)
Multiplying and dividing by 2
y=2/(2sinxcosx)
y=2/sin2x
If it is equal to 3/2, then
y=3/2
2/sin2x=3/2
4=3sin2x
Sin2x=4/3
Since siny cannot be greater than one but to satisfy to this condition siny must be greater than one but we get sin2x=4/3.
So, our first equation must be a contradiction.
So, tanx+cotx=!3/2( not possible)
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