Aug 12, 2015 · 2I = π∫π0 sinx 1 + cos2xdx. ⇒ I = π 2∫π0 sinx 1 + cos2xdx. Now assume that cosx = z ⇒ − sinx = dz. Now replace the variables and the according limits in your integral. i.e. I = π 2∫π0 − z 1 + z2dz. Then it is nothing difficult to find the result. Share. Cite. Dec 13, 2016 · cos2x + cosx − 1 = 0 we obtain. cosx = 1 2( − 1 ± √5). and. sinx = √ 1 2( − 1 + √5) Putting this results into the big equation. sin12x + ⋯ + sin6x we obtain the answer. Example. (√ 1 2( − 1 + √5))16 = 1 2 (47 −21√5) so the answer is. If tan(α+iβ) =eiθ ; where α,β ∈ R, θ ≠(2n+1)π 2,n ∈ Z and i =√−1, then. If the equation 4sin(x+ π 3)cos(x − π 6) =a2 +√3sin2x−cos2x has a solution, then the value of a can be. If f (x) = cosx [x π]+ 1 2, where x is not an integral multiple of π and [.] denotes the greatest integer function, then. Sep 26, 2016 · Explanation: This is a cubic equation in cos x. Sum of the coefficients is 0. So, cos x = 1 is a solution. The other factor is (cos x + 1)^2. It follows that the other two solutions are cosx = − 1, − 1. Easily, x ∈ [0.2π] are 0, pi and 2pi#. x=0, pi and 2pi. This is a cubic equation in cos x. integral 1/cos^2x. en. Related Symbolab blog posts. My Notebook, the Symbolab way. Math notebooks have been around for hundreds of years. You write down problems How do you verify #cos 2x = (1-tan^2x)/(1+tan^2x)# using the double angle identity? How do you use find the exact value of cos2x, given that cotx = -5/3 with pi/2EYuXz.