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Solution. Observe that $2\cos 4x\cos x = \cos 5x + \cos 3x$ by the sum-to-product formulas. Defining $a = \cos 3x$ and $b = \cos 5x$ , we have $a^3 + b^3 ... < Sux, cos 3x >. = -H. This stooks that as 3+. =0. 0 other. Fucher in V. F(I = 6) ... cos 3x unti. Vo es x)dx = 0. Page 2. (iv) the. ORTHOGONAL PROJECTION. PCA ... sa sinu du= -cosu+ (= - cos/√x) + C. U=3x du=3dx. 4S JX. U=√x dur 24/7 dx. 5. S cos(3x) dx. { sinu +(= {} sn13x |. 6. $ et dz. S =}{} cosu dy = = sinu + C =. Yp = -9 A Cos 3x-9B Sin 3x. Plug into ODE: (-9A (os 3x-98 Sin 3x)+4(-3A Sin 3x + 3B Cos3x). + 4 CA Cos 3x + B Sin 3x). = [-5A ]. T-5. +12B Cos 3x + -12A-5B ... Cos3x is an important identity in trigonometry, which is used to determine the value of the cosine function for an angle that is thrice the measure of angle x. This comes from the pythagorean theorem. You can convert the sides into measurements: s1²+s2²=h². Divide each side by h², and you will see that the terms can be ... Differentiate wrt x \sin(x)\left(121\left(\sin(x)\right)^{2}\left(\cos(x)\right)^{4}-75\left(\cos(x)\right)^{2}\left(\sin(x)\right)^{ If ∫sinxsin3x+cos3xdx=αloge|1+tanx|+βloge|1−tanx+tan2x|+γtan−1(2tanx−1√3)+C, where C is constant of integration, then the value of 18(α+β+γ2) is · | · | · | · | ... ... (cos(x) In (wing)) dx. 1'(x)=-mi(3x) - 3. In (mix) + cos(3x). (3x).3. fox. +63(3X) cos x. Sari X. (6713x)) co>x. SmiX. (s) (3X). (smi x. 3 . (sm (3x)) In (smix) ... Dec 16, 2014 ... 3x. 3x cos 3x. 1x 5. (b) (4 marks) lim q14= +0--2. ما. Page 10. 201-NYA-05 Calculus 1 Science. Final Exam A- Page 10 of 15. December 16th 2014.