The expression as a single trigonometric function is [tex]tan(\pi/35)[/tex]
What are trigonometric function?
"Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
There are a number of trigonometric formulas and identities that denotes the relation between the functions and help to find the angles of the triangle".
Given, the function
[tex]\frac{tan\frac{3\pi}{7} -tan \frac{2\pi}{5}}{1 + tan\frac{3\pi}{7}tan\frac{2\pi}{5} }[/tex]
[tex]tan(A-B) = (tan A - tan B)/1 + tan A tan B[/tex]
Now,
[tex]\frac{tan\frac{3\pi}{7} -tan \frac{2\pi}{5}}{1 + tan\frac{3\pi}{7}tan\frac{2\pi}{5} } = tan(3 \pi/7 - 2\pi/5)[/tex]
=[tex]tan(\pi/35)[/tex]
Hence A is the correct option.
To know more about trigonometric functions here
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