Which expression is equivalent to
$
\frac{\tan 2x - \tan x}{1 + \tan 2x \tan x}
$? - HSC - SSCE Mathematics Extension 1 - Question 3 - 2016 - Paper 1
Question 3
Which expression is equivalent to
$
\frac{\tan 2x - \tan x}{1 + \tan 2x \tan x}
$?
Worked Solution & Example Answer:Which expression is equivalent to
$
\frac{\tan 2x - \tan x}{1 + \tan 2x \tan x}
$? - HSC - SSCE Mathematics Extension 1 - Question 3 - 2016 - Paper 1
Identify the expression
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
We need to find an expression that is equivalent to ( \frac{\tan 2x - \tan x}{1 + \tan 2x \tan x} ).
Rewrite the numerator using the tangent subtraction formula
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Using the tangent subtraction formula, we can express ( \tan 2x - \tan x ) as ( \frac{\tan 2x - \tan x}{1 + \tan 2x \tan x} = \tan(x) ).
Final answer
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Thus, the expression equivalent to ( \frac{\tan 2x - \tan x}{1 + \tan 2x \tan x} ) is (A) ( \tan x ).
Join the SSCE students using SimpleStudy...
97% of StudentsReport Improved Results
98% of StudentsRecommend to friends
100,000+ Students Supported
1 Million+ Questions answered