How do you prove # tan^2x / (secx - 1) = secx + 1 #?
2 Answers
Hint :
Explanation:
To prove
Use the identity
We can rewrite this as
Now back to our problem
LHS
Recall the difference of square rule
We need to apply that for
Therefore, LHS = RHS thus proved.
Start by deciding on the more difficult side to work on. In this case, it's the left side. Recall the Pythagorean trigonometric identity,
Left side:
#color(red)(tan^2x)/(secx-1)#
#(color(green)(sec^2x-1))/(secx-1)#
Since "
#((color(orange)(secx+1))(color(blue)(secx-1)))/(secx-1)#
You will notice that "
#((secx+1)color(red)cancelcolor(black)((secx-1)))/color(red)cancelcolor(black)((secx-1))#
#secx+1#
#:.# , LS#=# RS.