Verify the Following Identity?
Let's simplify: 3ABC = A^3 + B^3 + C^3 - (1/2)(A + B + C) * [(A^2 - 2 * A * B + B^2) + (B^2 - 2 * B * C + C^2) + (C^2 - 2 * C * A + A^2)] 3ABC = A^3 + B^3 + C^3 - (1/2)(A + B + C) * [ A^2 - 2AB + B^2 + B^2 - 2BC + C^2 + C^2 - 2CA + A^2] 3ABC = A^3 + B^3 + C^3 - (1/2)(A + B + C) * [ 2A^2 - 2AB + 2B^2 - 2BC + 2C^2 - 2CA ] 3ABC = A^3 + B^3 + C^3 - (1/2) * (A + B + C) * (2A^2 - 2AB + 2B^2 - 2BC + 2C^2 - 2CA) 3ABC = A^3 + B^3 + C^3 - (A + B + C) * (1/2) * (2A^2 - 2AB + 2B^2 - 2BC + 2C^2 - 2CA) 3ABC = A^3 + B^3 + C^3 - (A + B + C) * (A^2 - AB + B^2 - BC + C^2 - CA) 3ABC = A^3 + B^3 + C^3 - (A^3 - A^2B + AB^2 - ABC + AC^2 - CA^2 + BA^2 - AB^2 + B^3 - B^2C + BC^2 - ABC + CA^2 - ACB + CB^2 - BC^2 + C^3 - C^2A) 3ABC = A^3 + B^3 + C^3 - (A^3 - A^2B + AB^2 - 3ABC + AC^2 - CA^2 + BA^2 - AB^2 + B^3 - B^2C + BC^2 + CA^2 + CB^2 - BC^2 + C^3 - C^2A) 3ABC = A^3 + B^3 + C^3 - (A^3 + AB^2 - 3ABC + AC^2 - CA^2 - AB^2 + B^3 - B^2C + BC^2 + CA^2 + CB^2 - BC^2 + C^3 - C^2A) 3ABC = A^3 + B^3 + C^3 - (A^3 - 3ABC + AC^2 - CA^2 + B^3 - B^2C + BC^2 + CA^2 + CB^2 - BC^2 + C^3 - C^2A) 3ABC = A^3 + B^3 + C^3 - (A^3 - 3ABC - CA^2 + B^3 - B^2C + BC^2 + CA^2 + CB^2 - BC^2 + C^3) 3ABC = A^3 + B^3 + C^3 - (A^3 - 3ABC + B^3 - B^2C + BC^2 + CB^2 - BC^2 + C^3) 3ABC = A^3 + B^3 + C^3 - (A^3 - 3ABC + B^3 - B^2C + CB^2 + C^3) 3ABC = A^3 + B^3 + C^3 - (A^3 - 3ABC + B^3 + C^3) 3ABC = A^3 + B^3 + C^3 - A^3 + 3ABC - B^3 - C^3 3ABC = 3ABC <------ TRUE ====== free to e-mail if have a question
Verify the following identity?
a million) (a million/sin^2x / (cosx/sinx) = sinx/(sin^2x cosx) = a million/sinxcosx = cscx secx 2) 2cos^2 x + cosx - a million = 0 (2cosx - a million)(cosx + a million) = 0 cosx = a million/2 x = pi/3 x = 5pi/3 cosx = -a million x = pi
Verify the following identity:?
This is alot easier then it appears. Given this equation: (sin^2x/cosx) + cosx = secx we can rearrange to get this.. (sin^2x/cosx) + cosx = 1/cosx Now multiply both sides by cosx and we get: (sin^2x/cosx)*cosx + cosx*cosx = (1/cosx)*cosx Now cancel all the the cosx and we get sin^2x + cos^2x = 1 We have shown that the above equation can be manipulated to obtain the "mother" identity, thereby verifying it as true.
Verify the following identity?
cosec² x = 1 / sin² x cotan x = cos x / sin x <=> cosec² x / cotan x = (1 / sin² x) / (cos x / sin x) = (1 / sin² x) * (sin x / cos x) = 1 / (sin x * cos x) = (1 / sin x) * (1 / cos x) = sec x * cosec x X = cos x 2X² + X - 1 = 0 Delta = 1 + 4 * 2 * 1 = 9 Sqr (delta) = 3 X1 = (-1 - 3) / 4 = -4/4 = -1 X2 = (-1 + 3) / 4 = 2/4 = 1/2 cos x = -1 => x = 180° [360°] cos x = 1/2 => x = 60° [360°] or x = 300° [360°]
Verify the following identity...?
there is this formula , sin(A+B)=sinAcosB+cosAsinB =>sin(x+y)+sin(x-y)=(sinxcosy+cosxsiny... =>sin(x+y)+sin(x-y)=2sinxcosy good luck
Verify the following identity used in calculus: [cos(x+h) - cos x]/h = [cos x(cos h-1)]/h]- [sin x sin h]/h?
From LHS: [cos(x+h) - cos x]/h = ( cos x cos h - sin x sin h - cos x ) / h = ( cos x cos h - cos x - sin x sin h ) / h = [ cos x(cos h-1) - sin x sin h ] / h = [cos x(cos h-1)]/h ]- [sin x sin h]/h (verified)
Verify the Following Trigonometric Identity!!!?
Recall that: sec²(x) - tan²(x) = 1 -tan²(x) = 1 - sec²(x) tan²(x) = sec²(x) - 1 csc²(x) - cot²(x) = 1 -cot²(x) = 1 - csc²(x) For the LHS (Left Hand Side), transform each identity into the expression that I solved for you: sec²(x) - 1 + 1 - csc²(x) ==> sec²(x) - csc²(x) Therefore, tan²(x) - cot²(x) = sec²(x) - csc²(x) (as LHS = RHS) I hope this helps!
Verify the following identity: cot(x - pi/2)= -tanx?
cot(x - π/2) = -cot(π/2 - x) = -tan(x) (Cofunction identity)
Verify the following identity. Assume all quantities are defined.?
sin α cos β + cos α sin β sin α cos β - cos α sin β Sum = 2 sin α cos β
Verify the following trigonometric identity step by step?
finish the right equation to make it equal to the left equation. So I do the right equation first: (1-cosec^2 t) / (cosec^2 t) = (-cotg2 t) / (cosec^2 t) ------> because 1 + cotg^2 t = cosec^2 t = (-1/tan^2 t) / (1/sin^2 t) -----> remember cotg (t) = 1 / tan t ---> so: cotg^2 t = 1/ tan^2 t and cosec (t) = 1/ sin t ---> so: cosec^2 t = 1/sin^2 t = (-1/tan^2 t)*(sin^2 t) = -(sin^2 t)/ tan^2 t = (-sin^2 t) * (sin^2 t/ cos^2 t) ------> we know : sin t/ cos t = tan t so: tan^2 t = sin^2 t/ cos^2 t = -cos^2 t = -(1/sec^2 t) = (-1)/(sec^2 t)