Q&A Prove that: cos(π/15) cos(2π/15) cos(3π/15) cos(4π/15) cos(5π/15) cos(6π/5) cos(7π/15) = 1/128 \cos\dfrac{\pi}{15} \cos\dfrac{2\pi}{15} \cos\dfrac{3\pi}{15} \cos\dfrac{4\pi}{15} \cos\dfrac{5\pi}{15} \cos\dfrac{6\pi}{15} \cos\dfrac{7\pi}{15}=\dfrac{1}{128}
Q&A Prove the equality\cos^2\dfrac{\pi}{8}+\cos^2\dfrac{3\pi}{8}+\cos^2\dfrac{5\pi}{8}+\cos^2\dfrac{7\pi}{8}=2
Q&A If A,B,C are three internal angles of a triangle, show that\sin^3 A \cos (B – C) + \sin^3 B \cos (C – A) + \sin^3 C \cos (A – B) = 3 \sin A \sin B \sin C
Q&A Show that \tan 18\degree =\tan 6\degree \cdotp \tan(60\degree - 6\degree )\cdotp \tan(60\degree + 6\degree )
Q&A Find the value of \cos \dfrac{π}{7}+ \cos\dfrac{3π}{7}+ \cos\dfrac{π}{57} cos(π/7) + cos(3π/7) + cos(5π/7)
Q&A For any triangle ABC, prove that cot (A/2)+cot(B/2)+cot(C/2) = cot(A/2)cot(B/2)cot(C/2)\cot\dfrac{A}{2}+ \cot\dfrac{B}{2}+\cot\dfrac{C}{2} = \cot\dfrac{A}{2}\cot\dfrac{B}{2}\cot\dfrac{C}{2}
Q&A If \triangle ABC has inradius r amd circumradius R, show thatr = 4R\sin{\dfrac{A}{2}} \sin{\dfrac{B}{2}} \sin{\dfrac{C}{2}} r=4Rsin(A/2)sin(B/2)sin(C/2)
Q&A If \cosα+\cosβ+\cosγ=0 and \sinα+\sinβ+\sinγ=0, find the value of \cos(α-β) + \cos(β-γ) + \cos(γ - α)
Q&A Find exact value of \sin\dfrac{\pi}{7} \sin\dfrac{2\pi}{7} \sin\dfrac{3\pi}{7} or sin(pi/7)sin(2pi/7)sin(3pi/7)
Multiple choice If α and β are angles in the first quadrant \tanα=\dfrac{1}{7}, \sinβ=\dfrac{1}{\sqrt{10} } , then the value of α+2β is
