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Class : XI Holiday AssignmentSubject : Mathematics Chapter : Trigonometry If tanθ = ab, then find the value of asin2θ+ bcos2θ. Find the value of 2+2+2cos4θIf (3sinθ + 5cosθ) =5, then find the value of (5sinθ - 3cosθ)Prove that: 2 cos π13 cos 9π13 + cos 3π13 +cos 5π13 = 0Find the general solution of cos3x + cosx + cos2x = 0.Show that sin10.sin50.sin60.sin70 = 316Find the principal solution of the equation : sin x= - 32 Prove that: sin5x-2sin3x+sinxcos5x-cosx = tanxProve that: cos 2x cosx2 – cos3x.cos9x2 =sin5x.sin5x2Find the general solution of the equation: sin2x + sin4x + sin6x = 0If x and y are acute angles such that sinx = 15 and siny = 110 find the value of sin(x+y).Prove that : cos2x + cos2x+π3 + cos2x-π3 = 32Prove that: (i) sin1050+ cos1050 = 12 (ii) tan560 = cos110+sin110cos110-sin110If tanx = -4 3, π2<x<π, find the values of sin x2 , cos x2 and tan x2 Find the principal solution of the equation : cot x = - 3Prove that: sin6000tan-6900+sec8400 cot-9450=32If x and y are acute angles such that cos x=1314 and cos y =17 , then prove that cos(x-y) = 12If cosα + cosβ = 0 = sinα + sinβ, prove that cos2α + cos2β = -2cos?(α+β).Solve the equation: 4sinxcosx + 2sinx + 2cosx + 1 = 0If cos x = -13 and x lies in quadrant III, find the values of sin x2, cos x2 and tan x2.Solve the equation: 2tanx – cotx + 1= 0.Find the value of : sin (80+θ) cos (20+θ ) – cos (80+θ) sin (20+θ).Prove that:sin75?-sin15?cos75?+cos15?= 13.If a tanθ = b, then find the value of bsinθ-acosθbsinθ+acosθ .Find the general solution of : 2cos2x+3 sinx=0Show that : cos 105? + cos 15? = sin 75? - sin 15?Show that : 3 sin π6 sec π3-4sin5π6 cotπ4 =1 If sin θ= 2129 , show thatsec θ+tan θ= 2 12 , θ lying between 0 and π2. Prove that : cos 20°. cos40?. cos60? . cos80? = 116If tanx = 34 , x lies in third quadrant , find the values of sin x2 , cos x2 and tan x2 *************************************** ................
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