Write an algebraic expression that is equivalent to the give

Write an algebraic expression that is equivalent to the given expression. csc(arctan x/ (square root of 7))

Solution

csc(arctan x/ (square root of 7))

first let us say A= arc tan x/sqrt(7)

tanA = x/sqrt(7)

now we know tan tanA find cscA

Taking x as oppsite side and `sqrt(7)` as the adjacent side,the hypotenuse will be equal to `sqrt(x^2+7).

cscA = sqrt(x^2+7) / x

now csc(arctan x/ (square root of 7)) = csc(A)

= sqrt(x^2+7)/x