csc4x - cot4x = csc2x + cot2x
The numbers 4,4,2,2 are all supposed to be the fourth and the second
The numbers 4,4,2,2 are all supposed to be the fourth and the second
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If the 4's and 2's are exponents....
Factor csc^4(x) - cot^4(x) into their conjugates (it's a difference of squares):
[csc^2(x) + cot^2(x)] * [csc^2(x) - cot^2(x)] = csc^2(x) + cot^2(x)
Divide by csc^2(x) + cot^2(x):
csc^2(x) - cot^2(x) = 1
Rewrite the trig functions:
1/sin^2(x) - cos^2(x)/sin^2(x) = 1
Now, you have a common denominator. Combine the two fractions into one fraction:
[1 - cos^2(x)]/sin^2(x) = 1
Multiply both sides by sin^2(x):
1 - cos^2(x) = sin^2(x)
A basic trig identity is that sin^2(x) + cos^2(x) = 1. So add cos^2(x) to both sides:
1 = sin^2(x) + cos^2(x)
1=1
That's it. :D
Factor csc^4(x) - cot^4(x) into their conjugates (it's a difference of squares):
[csc^2(x) + cot^2(x)] * [csc^2(x) - cot^2(x)] = csc^2(x) + cot^2(x)
Divide by csc^2(x) + cot^2(x):
csc^2(x) - cot^2(x) = 1
Rewrite the trig functions:
1/sin^2(x) - cos^2(x)/sin^2(x) = 1
Now, you have a common denominator. Combine the two fractions into one fraction:
[1 - cos^2(x)]/sin^2(x) = 1
Multiply both sides by sin^2(x):
1 - cos^2(x) = sin^2(x)
A basic trig identity is that sin^2(x) + cos^2(x) = 1. So add cos^2(x) to both sides:
1 = sin^2(x) + cos^2(x)
1=1
That's it. :D