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Popular >

simplify cos(arctan(x)+arctan(x))

Solution

simplify

cos (arctan (x) + arctan (x))

Solution

\frac{1 - x ^{2}}{1 + x ^{2}}

Solution steps

cos (arctan (x) + arctan (x))

Rewrite using trig identities

= cos^{2} (arctan (x)) - sin^{2} (arctan (x))

Use the following identity:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= (\frac{1 + x ^{2}}{1 + x ^{2}})^{2} - sin^{2} (arctan (x))

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= (\frac{1 + x ^{2}}{1 + x ^{2}})^{2} - (\frac{x 1 + x ^{2}}{1 + x ^{2}})^{2}

Simplify

= \frac{1 - x ^{2}}{1 + x ^{2}}

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Frequently Asked Questions (FAQ)

What is cos(arctan(x)+arctan(x)) ?
The solution to cos(arctan(x)+arctan(x)) is (1-x^2)/(1+x^2)