SOLUTION: Simplify the following problem. (sec^2x + csc^2x)-(tan^2x + cot^2x)

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Question 408166: Simplify the following problem.
(sec^2x + csc^2x)-(tan^2x + cot^2x)
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Simplifying the following:

(sec^2x + csc^2x)-(tan^2x + cot^2x)

tan^2x = sec^2x -1

cot^2x = csc^2x -1

(sec^2x + csc^2x)-(sec^2x -1 + csc^2x -1)= 2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28sec%5E2%28x%29+%2B+csc%5E2%28x%29%29-%28tan%5E2%28x%29+%2B+cot%5E2%28x%29%29


=sec%5E2%28x%29+%2B+csc%5E2%28x%29+-+tan%5E2%28x%29+-+cot%5E2%28x%29......sincesec%5E2x+=+tan%5E2%28x%29%2B1 you will have

=tan%5E2%28x%29+%2B+1+%2B+csc%5E2%28x%29+-+tan%5E2%28x%29+-+cot%5E2%28x%29


=

=1+%2B+csc%5E2x++-+cot%5E2x.........since csc%5E2%28x%29=cot%5E2%28x%29+%2B+1....=>...

=1+%2B+cot%5E2%28x%29+%2B+1++-+cot%5E2%28x%29

=1+%2B+cross%28cot%5E2%28x%29%29+%2B+1++-+cross%28cot%5E2%28x%29%29

=2+