Can you help me with these two problems? I have to use trig identities to transform one side of the equation into the other and I'm very confused. If you could explain how you got the answer, that would be great!
(1 + cos theta)(1 - cos theta) = sin^2 theta
sin^2 - cos^2 = 2sin^2 theta - 1
Evan
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For the first one, expand the binomials on the left side.
You can use the FOIL method, or whatever method you like best. (I'll use A for theta)
(1 + cosA)(1 - cosA) = sin^2 A
1 - cosA + cosA - cos^2 A = sin^2 A
1 - cos^2 A = sin^2 A
Using the pythagorean identity, we know that 1 - cos^2 A = sin^2 A. Therefore, the identity is proven.
For the second one, the pythagorean theorem is used again. Since we know that sin^2 A + cos^2 A = 1, we can insert it into the equation where there is a 1, which is on the right side.
sin^2 A + cos^2 A = 2sin^2 A - (sin^2 A + cos^2 A)
Now you just simplify the right side by adding and subtracting like terms
sin^2 A + cos^2 A = 2sin^2 A - sin^2 A - cos^2 A
sin^2 A + cos^2 A = sin^2 A - cos^2 A
Left side equals right side, therefore identity is true.
patel
tan O = sin O / cos O cot O = a million / tan O cot O = cos O / sin O tan O / cot O = (sin O / cos O) / (cos O / sin O) cancel out sin O in numerator and denominator = (a million / cos O) / (cos O / a million) cancel out cos O in numerator and denominator = (a million / a million) / (a million / a million) = a million / a million = a million