tan(tan-1 7.4)=?
obviously 7.4
By definition tan(tan−1(7.4))=7.4
More explicitly:
Let α=tan−1(7.4)
Then by definition α is the unique angle such that tanα=7.4 and −π2<α<π2.
To solve this equation, we can use the trigonometric identity: tan(tan^(-1)(x)) = x.
In this case, x is 7.4. So the equation becomes: tan(tan^(-1) 7.4) = 7.4.
To find the value of tan^(-1)(7.4), we need to use the inverse tangent function (also known as arctan or tan^(-1)) which gives us the angle whose tangent is equal to 7.4.
Using a calculator or a math software, we find that arctan(7.4) is approximately 1.402.
Now, we substitute this value back into the equation: tan(1.402) = 7.4.
Using a calculator or a math software, we find that tan(1.402) is approximately 8.14.
Therefore, tan(tan^(-1) 7.4) = 8.14.