13 years ago
Anonymous

trig identity help?

1-cos^2x + cot^2x-cos^2x(cot^2x)= 1
Top 2 Answers
13 years ago
Puzzling
Favorite Answer
You are trying to prove that: 1 - cos²x + cot²x - cos²x (cot²x) = 1 Start with: 1 - cos²x + cot²x - cos²x (cot²x) Pull out a common cot²x from the last two terms: 1 - cos²x + cot²x(1 - cos²x) The expression in the parentheses is equal to sin²x: 1 - cos²x + cot²x(sin²x) And cot²x = 1/tan²x = cos²x / sin²x: 1 - cos²x + (cos²x/sin²x)(sin²x) The sin²x terms cancel out: 1 - cos²x + cos²x And the cos²x terms cancel out 1 QED
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13 years ago
ironduke8159
1-cos^2x + cot^2x-cos^2x(cot^2x)= 1 -cos^2x + cot^2x-cos^2x(cot^2x)= 0 -1 + cot^2x/cos^2x - cot^2x = 0 -1+ 1/sin^2x - cos^2x/sin^2x = 0 -1 + (1-cos^2x)/sin^2x = 0 -1 +sin^2x/sin^2x=0 -1+1 = 0 0=0
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