Q. Prove that: (2cos2A-1)(2cos2A+1)(2cos4A-1)(2cos8-1)=2cos16A+1

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Q. The angle of elevation of an aeroplane from a point on the ground is 450. After 15 seconds of flight the angle of elevation changes to 300. If the aeroplane is flying horizontally at a height of 4000m in the same direction, find the speed of aeroplane. Soln: ...
If A, B, C and D are angles of a quadrilateral and sin(A/2).sin(B/2).Sin(C/2).sin(D/2) = 1/4, prove that A = B = C = D = pi/2 Soln: ...
Q. Find the angle between the lines represented by the equation (x^2 + y^2)sin^2a = (xcosa – ysina)^2. Soln: (x^2 + y^2)sin2a = (xcosa – ysina)^2 x2sin2a + y2sin2a = x2cos2a – 2xycosa.sina + y2sin2a (sin2a – cos2a)x2 + 2x ...
Prove that: (sin3Acos2A-cos3ASin2A)/(cos3Acos2A+sin3Asin2A) = TanA L.H.S =(sin3Acos2A-cos3ASin2A)/(cos3Acos2A+sin3Asin2A) =(sin(3A-2A))/(cos(3A-2A) =sinA/cosA =tanA ...
Prove that: (sec^2A+1)(sec^4A+1)(sec^8A+1)=tan8A.cotA Soln: ...