Q. Prove that: 4(cos^4A+sin^4A)/(cos^4A-sin^4A)=(3+cos4A)Sec2A

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Q. If (-4,3) and (2,5) are pair of opposite vertices of a square. Find the equations of the diagonals of the square. Soln: The equation of diagonal BD is given by as, y-y1 = (y2-y1)/(x2-x1)*(x-x1) Here, x1 = -4, y1 = 3 and x2 = 2 ...
Q. Prove that: sec2A+tan2A=tan(45+A) L.H.S. = 1 / cos(2a) + sin(2a) / cos(2a) = (1 + sin(2a)) / (cos(2a)) = (sin^2(a) + cos^2(a) + 2 * sin(a) * cos(a)) / (cos^2(a) - s ...
Prove that: (sin3Acos2A-cos3ASin2A)/(cos3Acos2A+sin3Asin2A) = TanA L.H.S =(sin3Acos2A-cos3ASin2A)/(cos3Acos2A+sin3Asin2A) =(sin(3A-2A))/(cos(3A-2A) =sinA/cosA =tanA ...
Q. If f(x) = x^2 – 2x, g(x) = 2x + 3 and fg-1(x) = 3 then find the value of x. Soln: To find g-1(x), Let y be the image of x under g, then y = 2x + 3 x = (y – 3)/2 Interchanging the role of x and y, we ha ...
Q. f(4x+5)=12x+18 , find the f'(x) Soln: Let 4x + 5 = a or, x = (a-5)/4 Then, f(a) = 12*(a - 5)/4 + 18 = 3*(a - 5) ...