SOLUTION: I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged.
1/1+co
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Question 325256: I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged.
1/1+cos theta + 1/1-cos theta = 2 + 2 cot^2 theta
I can make each side equal 2csc^2 theta currently, but have no clue how to make them equal working only one side. Thanks for taking the time to look at this, its appreciated.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
}+\frac{1}{1-\cos(\theta)}=2+2\cot^2{\theta})
... Start with the given equation.
}{(1+\cos(\theta)(1-\cos(\theta))}+\frac{1}{1-\cos(\theta)}=2+2\cot^2{\theta})
... Multiply the first fraction by
}{(1+\cos(\theta)(1-\cos(\theta))}+\frac{1+\cos(\theta)}{(1+\cos(\theta)(1-\cos(\theta))}=2+2\cot^2{\theta})
... Multiply the second fraction by
)+(1+\cos(\theta))}{(1+\cos(\theta)(1-\cos(\theta))}=2+2\cot^2{\theta})
... Add the fractions.
(1-\cos(\theta))}=2+2\cot^2{\theta})
... Combine like terms.
}=2+2\cot^2{\theta})
... FOIL the denominator.
}=2+2\cot^2{\theta})
... Use the identity  = 1-\cos^2(\theta))
}=2+2\cot^2{\theta})
... Rewrite 2 as 2*1
+\cos^2(\theta)\right)}{\sin^2(\theta)}=2+2\cot^2{\theta})
... Use the identity +\cos^2(\theta) = 1)
(replace the "1" with the left side)
+2\cos^2(\theta)}{\sin^2(\theta)}=2+2\cot^2{\theta})
... Distribute.
}{\sin^2(\theta)}+\frac{2\cos^2(\theta)}{\sin^2(\theta)}=2+2\cot^2{\theta})
... Break up the fraction.
... Reduce and use the identity
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