Fill in the blank !! question in picture below i have no clue what to do
1 answer:
(tanx)^2 Proof: Verify the following identity: (sec(x) - 1) (sec(x) + 1) = tan(x)^2 Write secant as 1/cosine and tangent as sine/cosine: (1/cos(x) - 1) (1/cos(x) + 1) = ^? (sin(x)/cos(x) )^2 (sin(x)/cos(x))^2 = (sin(x)^2)/(cos(x)^2): (1/cos(x) - 1) (1/cos(x) + 1) = ^?(sin(x)^2)/(cos(x)^2) Put 1/cos(x) - 1 over the common denominator cos(x): 1/cos(x) - 1 = (1 - cos(x))/cos(x): (1 - cos(x))/cos(x) (1/cos(x) + 1) = ^?(sin(x)^2)/(cos(x)^2) Put 1/cos(x) + 1 over the common denominator cos(x): 1/cos(x) + 1 = (cos(x) + 1)/cos(x): (1 - cos(x))/cos(x) (cos(x) + 1)/cos(x) = ^?(sin(x)^2)/(cos(x)^2) ((1 - cos(x)) (cos(x) + 1))/(cos(x) cos(x)) = ((1 - cos(x)) (cos(x) + 1))/cos(x)^2: ((1 - cos(x)) (cos(x) + 1))/(cos(x)^2) = ^?(sin(x)^2)/(cos(x)^2) Multiply both sides by cos(x)^2: (1 - cos(x)) (cos(x) + 1) = ^?sin(x)^2 (1 - cos(x)) (cos(x) + 1) = 1 - cos(x)^2: 1 - cos(x)^2 = ^?sin(x)^2 sin(x)^2 = 1 - cos(x)^2: 1 - cos(x)^2 = ^?1 - cos(x)^2 The left-hand side and right-hand side are identical: Answer: (identity has been verified)
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Step-by-step explanatio
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