How do you simplify #tan^2x(csc^2x-1)#?

Question

15354 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-26T08:10:03

By using the Trigonometric Identity : #sin^2x+cos^2x=1#

Divide both sides of the above identity by #sin^2x# to obtain,

#sin^2x/(sin^2x)+cos^2x/sin^2x=1/sin^2x#

#=>1+1/(sin^2x/cos^2x)=csc^2x#

#=>1+1/tan^2x=csc^2x#

#=>csc^2x-1=1/tan^2x#

Now, we are able to write : #tan^2x(csc^2x-1)" "# as #" "tan^2x(1/tan^2x)#

and the result is #color(blue)1#

Answer 2 · 2015-07-27T04:22:48

Simplify: #tan^2 x(csc^2 x - 1)#

#sin^2 x/cos^2x(1/sin^2 x - 1) = (sin^2 x/cos^2 x)((1 - sin^2 x)/sin^2 x) = #

#= sin^2 x/cos^2 x(cos^2 x /sin^2 x)# = 1.