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- [[Euler's identity]] states that <math>e^{ix} = \cos (x) + i \sin(x)</math>. We have that To derive the tangent addition formula, we reduce the problem to use sine and cosine, divide both8 KB (1,397 words) - 20:55, 20 January 2024
- ...}}{1+\sin{\theta}\cos{\theta}}</math>. Squaring and using the double angle identity for sine, we get, <math>110(\sin{2\theta})^2 + \sin{2\theta} - 1 = 0</math> Identity, and then use the tangent double angle identity. Thus, <math>\tan{\theta} = 10-3\sqrt{11}</math>. Substituting into the ori5 KB (838 words) - 17:05, 19 February 2022
- ...\theta = BD</math> and <math>\tan 2 \theta = 2</math>. By the double angle identity, <cmath>2 = \frac{2 BD}{1 - BD^2} \implies BD = \boxed{\frac{\sqrt5 - 1}{2} Remarks: You could also use tangent half angle formula2 KB (376 words) - 11:50, 10 August 2024
- ...zeros and the function is never negative, all <math>3</math> zeros must be double roots because the function's degree is <math>6</math>. We also know that this graph has 3 places tangent to the x-axis, which means that each root has to have a multiplicity of 2.6 KB (1,056 words) - 16:45, 26 August 2024
- Let <math>x = \cos 1^\circ + i \sin 1^\circ</math>. Then from the identity <math>=\sqrt{\frac{1}{2^{89}}}</math> because of the identity <math>\sin(90+x)=\cos(x)</math>11 KB (1,634 words) - 18:51, 18 February 2025
- Using the definition of tangent, Finally, by using the Double Angle Identity for Tangent,1 KB (184 words) - 13:00, 20 February 2020
- ...f a line connecting a point on the circle to the origin. That line must be tangent to the circle. ...), we find that <math>\tan \theta = \frac13</math>. Using the Double Angle Identity yields <math>\tan 2\theta = \frac34</math>, so <math>\tan (90 - 2\theta) =4 KB (722 words) - 19:53, 27 March 2019
- ...the desired half-angle identities for sine and cosine. As for the tangent identity, divide the sine and cosine half-angle identities.956 bytes (149 words) - 19:23, 7 September 2023
- Now, we can take the tangent and apply the tangent subtraction formula: Following from the double-angle identity, we have14 KB (2,223 words) - 13:27, 1 September 2024
- {{shortcut|[[Trig identity proof]]}} =Double angle formulas=19 KB (3,268 words) - 20:55, 4 February 2025