Statement 1 - If θ ∈ ( 3 π , 2 π ) then tan θ c o t θ cot θ t a n θ . Statement 2 - The function x 1/ x decreases for all x 3 .

Question

Statement 1 - If θ ∈ ( 3 π ​ , 2 π ​ ) then tan θ c o t θ > cot θ t a n θ . Statement 2 - The function x 1/ x decreases for all x > 3 .

TestHub · Accepted Answer

f ( x ) = x 1/ x decreases for x > e . For θ ∈ ( 3 π ​ , 2 π ​ ) ⊂ ( 0 , … ) we have tan θ > 1 > cot θ > 0 , so ( tan θ ) c o t θ > 1 > ( cot θ ) t a n θ and Statement 1 is true. Statement 2 is true (since 3 > e ) but does not explain Statement 1, which needs only tan θ > 1 > cot θ .

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