Math, asked by dahiyasachin2005, 8 months ago

Prove that tan x + cot X can never be equal to 3/2​

Answers

Answered by maliana36
4

Answer:

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Answered by thanushiya72
1

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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