Question

If \[\tan x = - 1.5\], what is the value of \[\tan \left( { - x} \right)\]?

Answer 1

Hint: We need to find the value of \[\tan \left( { - x} \right)\] when we are given the value of \[\tan x\]. We need to recall the formulas of trigonometry. We know, \[\tan x\] satisfies \[\tan \left( { - x} \right) = - \tan x\]. So, to solve this question, we will make use of this property and proceed further to reach our answer.

Complete step-by-step answer:
We are given \[\tan x = - 1.5\]
We need to find the value of \[\tan \left( { - x} \right)\].
We know,
\[\tan \left( { - x} \right) = - \tan \left( x \right)\]
Using \[\tan \left( x \right) = - 1.5\] in the above equation, we get
\[ \Rightarrow \tan \left( { - x} \right) = - \tan \left( x \right)\]
\[ \Rightarrow \tan \left( { - x} \right) = - \tan \left( x \right) = - \left( { - 1.5} \right)\]
Which implies that,
\[ \Rightarrow \tan \left( { - x} \right) = - \left( { - 1.5} \right)\]
Now, using \[ - \left( { - f\left( x \right)} \right) = f\left( x \right)\], we get
\[ \Rightarrow \tan \left( { - x} \right) = 1.5\]
Hence, we get,
If \[\tan \left( x \right) = - 1.5\], then the value of \[\tan \left( { - x} \right)\] is \[1.5\].

Note: We need to remember that out of all the trigonometric functions, only cosine and secant do not satisfy that trigonometric function with negative angle \[\theta \] is equal to negative of the trigonometric function with positive angle \[\theta \]. Also, we need to note that negative of a negative function is positive and negative of a positive function is negative.