Statement 1 - The inequality lo g s i n x 2 t a n x 0 has no real roots in the interval ( 0 , 2 π ) . Statement 2 - The domain of the function f ( x ) = lo g s i n x 2 t a n x is ⋃ n ∈ Z ( 2

Question

Statement 1 - The inequality lo g s i n x ​ 2 t a n x > 0 has no real roots in the interval ( 0 , 2 π ​ ) . Statement 2 - The domain of the function f ( x ) = lo g s i n x ​ 2 t a n x is ⋃ n ∈ Z ​ ( 2 nπ , 2 nπ + 2 π ​ ) .

TestHub · Accepted Answer

For x ∈ ( 0 , 2 π ) , 0 < sin x < 1 and 2 t a n x > 1 , so lo g s i n x 2 t a n x < 0 . There is no root, so Statement 1 is true. The domain needs sin x > 0 , sin x  = 1 , cos x  = 0 along with tan x defined, so it is ⋃ ( 2 nπ , 2 nπ + π ) without x = 2 nπ + 2 π , and Statement 2 is false.

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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