Factor the algebraic expression below in terms of a single trigonometric function. csc^2x - 1

Question

Factor the algebraic expression below in terms of a single trigonometric function.  csc^2x - 1

sidsiddhartha · Answer

cscx=1/sinx
csc^x-1=1/sin^2x-1=(1-sin^2x)/sin^2x=cos^2x/sin^2x=cot^2x

anonymous · Answer

...Wow, I'm totally lost. -shakes head.- Okay, let me try to trace over what you did. First off. $$\csc ^{2}x - 1 $$ Then. You do.. $$\csc x-1 =1 \div \sin^2-1 $$ But why and how?

sidsiddhartha · Answer

sorry it's
csc^2x-1=(1/sin^2x)-1

anonymous · Answer

Okay, so since 1/sin^2x is the reciprocal function. Thats how you got it, simply switching around. But why would you divide it by sin and where does the -1 go to?

sidsiddhartha · Answer

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