Cot^2x-csc^2x
Please help me simplify using identities! Thank You!
Now this is just like the other one
(cos x/sin x)^2 - (1/sin x)^2
= (cos^2 x - 1)/sin^2x
= sin^2 x / sin^2x
= 1
that's -1
remember
sec^2 = 1+tan^2
csc^2 = 1+cot^2
these come from dividing
1 = sin^2+cos^2
by cos^2 or sin^2
To simplify the expression cot^2(x) - csc^2(x) using trigonometric identities, we'll need to use the Pythagorean identities for cotangent and cosecant.
The Pythagorean identity for cot^2(x) states:
cot^2(x) = 1 + csc^2(x)
And the Pythagorean identity for csc^2(x) states:
csc^2(x) = 1 + cot^2(x)
Using these identities, we can substitute these values into our original expression:
cot^2(x) - csc^2(x) = (1 + csc^2(x)) - (1 + cot^2(x))
Next, we can simplify the expression further:
= 1 + csc^2(x) - 1 - cot^2(x)
The 1 and -1 terms cancel out, and we're left with:
= csc^2(x) - cot^2(x)
So, cot^2(x) - csc^2(x) simplifies to csc^2(x) - cot^2(x).