SOLUTION: Q1)if a sinēθ+b cosēθ =c then prove that: tan θ=√c-b/a-c

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Question 1083721: Q1)if a sinēθ+b cosēθ =c
then prove that: tan θ=√c-b/a-c
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if a*sin^2 + b*cos^2 = c
then prove that: tan = sqrt((c-b)/(a-c))
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a*sin^2 + b*cos^2 = c
a*sin^2 + a*cos^2 + (b-a)*cos^2 = c
a + (b-a)*cos^2 = c
cos^2 = (a-c)/(a-b)
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a*sin^2 + b*cos^2 = c
a*sin^2 - b*sin^2 + b*cos^2 + b*sin^2 = c
sin^2*(a-b) + b = c
sin^2 = (c-b)/(a-b)
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tan^2 = sin^2/cos^2
tan^2 = ((c-b)/(a-b))/((a-c)/(a-b))
tan^2 = (c-b)/(a-c)
tan = sqrt%28%28c-b%29%2F%28a-c%29%29