SOLUTION: Please help me to prove that tan^2(x) - sin^(x) = tan^(x) sin^2(x)
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Question 130978: Please help me to prove that tan^2(x) - sin^(x) = tan^(x) sin^2(x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's manipulate the left side to transform it into the right side (note: we are not going to even touch the right side)
-\sin^2\left(x\right))
.... Start with the left side
}{\cos^2\left(x\right)}-\sin^2\left(x\right))
.... Rewrite )
as }{\cos^2\left(x\right)})
}{\cos^2\left(x\right)}-\sin^2\left(x\right)\left(\frac{\cos^2\left(x\right)}{\cos^2\left(x\right)\right))
.... Multiply )
by }{\cos^2\left(x\right)})
}{\cos^2\left(x\right)}-\frac{\sin^2\left(x\right)\cos^2\left(x\right)}{\cos^2\left(x\right)})
.... Multiply
-\sin^2\left(x\right)\cos^2\left(x\right)}{\cos^2\left(x\right)})
.... Combine the fractions.
\left(1-\cos^2\left(x\right)\right)}{\cos^2\left(x\right)})
.... Factor out
\left(sin^2\left(x\right)\right)}{\cos^2\left(x\right)})
.... Replace )
with
\sin^2\left(x\right))
.... Replace with
So this shows us that
-\sin^2\left(x\right)=\tan^2\left(x\right)\sin^2\left(x\right))
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