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Which of the following statements about tan 10 ° is true? 1. It is a rational number2. It is an irrational number less than 23. It is an irrational number greater than 24. It is greater than 2

Shravan Kumar , 5 Years ago
Grade 10
anser 2 Answers
Arun

Last Activity: 5 Years ago

Dear student
 
as we know tan 45 degree = 1
hence tan 10 degree will be less than 1 as tan is increasing function.
 
also it is irrational number

Mohitnagaraj

Last Activity: 4 Years ago

Solution : 
Since tan θ is an increasing function on (0,π/2)
∴tan10∘
Thus option (c ) is true.
Now, tan30∘=3tan10∘−tan310∘1−3tan210∘
If tan10∘ is a trational number, then 3tan10∘−tan310∘1−3tan210∘ must be a rational number, which is not true,
Hence, tan10∘ is an irrational number.

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