SOLUTION: instruction: show that the following will give the value of 1. prob. 1. (csc x - cot x)(csc x + cot x) prob. 2. 1 divided by 1 + tan squared x + 1 divided by cot squared x

Question 396065: instruction: show that the following will give the value of 1.
prob. 1. (csc x - cot x)(csc x + cot x)
prob. 2. 1 divided by 1 + tan squared x + 1 divided by cot squared x + 1
prob. 3. 1 - sin squared x divided by cos squared x.

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
instruction: show that the following will give the value of 1.
prob. 1. (csc x - cot x)(csc x + cot x)
prob. 2. 1 divided by 1 + tan squared x + 1 divided by cot squared x + 1
prob. 3. 1 - sin squared x divided by cos squared x.

sohcahtoa:
sin = opp/hyp, cos = adj/hyp, tan = opp/adj,
tan = sin/cos, cot = 1/tan = cos/sin,
csc = 1/sin, sec = 1/cos,
sin^2 + cos^2 = 1, 1 + tan^2 = sec^2, 1 + cot^2 = csc^2

prob. 1. (csc x - cot x)(csc x + cot x)
(csc x - cot x)(csc x + cot x)
(1/(sin x) - (cos x)/(sin x))(1/(sin x) + (cos x)/(sin x))
by FOIL (First Outer Inner Last) middle terms are gonna cancel out
1/(sin^2 x) - (cos^2 x)/(sin^2 x)
(1 - cos^2 x)/(sin^2 x)
(sin^2 x)/(sin^2 x)
1
prob. 2. 1 divided by 1 + tan squared x + 1 divided by cot squared x + 1
1/(1 + tan^2 x) + 1/(cot^2 x + 1)
1/(sec^2 x) + 1/(csc^2 x)
cos^2 x + sin^2 x
1
prob. 3. 1 - sin squared x divided by cos squared x.
(1 - sin^2 x)/(cos^2 x)
(cos^2 x)/(cos^2 x)
1

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