Prove? #cscx(1+cosx)(cscx-cotx)=1#
3 Answers
See explanation
Explanation:
We will use the following:
#(a+b)(a-b) = a^2-b^2# #csc(x) = 1/sin(x)# #cot(x) = cos(x)/sin(x)# #1-cos^2(x) = sin^2(x)#
With those,
#= (csc(x)+cot(x))(csc(x)-cot(x))#
#=csc^2(x)-cot^2(x)#
#=1/sin^2(x)-cos^2(x)/sin^2(x)#
#=(1-cos^2(x))/sin^2(x)#
#=sin^2(x)/sin^2(x)#
#=1#
proved
See below:
Explanation:
We have:
distributing out:
and now to reorder and simplify:
Now we'll use the identity of