What is taylor (cos^2(2θ))/(cos(θ)) ?

The answer to taylor (cos^2(2θ))/(cos(θ)) is 1-7/2 θ^2+85/24 θ^4+\ldots

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taylor (cos^2(2θ))/(cos(θ))

taylor

\frac{cos ^{2} ( 2 θ )}{cos ( θ )}

1 - \frac{7}{2} θ^{2} + \frac{85}{24} θ^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d θ} ( \frac{c o s ^{2} ( 2 θ )}{c o s ( θ )} ) ( 0 )}{1 !} θ + \frac{\frac{d ^{2}}{d θ ^{2}} ( \frac{c o s ^{2} ( 2 θ )}{c o s ( θ )} ) ( 0 )}{2 !} θ^{2} + \frac{\frac{d ^{3}}{d θ ^{3}} ( \frac{c o s ^{2} ( 2 θ )}{c o s ( θ )} ) ( 0 )}{3 !} θ^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} θ + \frac{- 7}{2 !} θ^{2} + \frac{0}{3 !} θ^{3} + \frac{85}{4 !} θ^{4} + \dots

Refine

= 1 - \frac{7}{2} θ^{2} + \frac{85}{24} θ^{4} + \dots

What is taylor (cos^2(2θ))/(cos(θ)) ?
The answer to taylor (cos^2(2θ))/(cos(θ)) is 1-7/2 θ^2+85/24 θ^4+\ldots