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Why does tanx = sinx/cosx ?

This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse sides O...
SR
16103 Views

Write (1+2i) /(2-i) in form x+iy

(1+2i) (2+i)/(2+i)(2-i) = (2-2+4i+i)/5 = 5i/5 = i
RM
3374 Views

Find the eigenvalues for the matrix (4/2/3,2/7/0,-2/1/8)

8,5,6Add '-x-' to each of the three terms on the leading diagonalCalculate the determinant of the 3x3 matrix and set equal to zero (property of eigenvalues)Factorise to find values of x, for which the determ...
TD
2956 Views

Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)

Vector joining the two lines = (1, 5, 6) - (1, 7, -3) = (0, -2, 9)Normal vector to the two lines = (-2, -1, 0) x (2, 0, 4) = (-4, 8, 2) = 2(-2, 4, 1)Hence, using the dot product, shortest distance = (0, -2, ...
AH
2986 Views

(x+4)((x^2) - kx - 5) is expanded and simplified. The coefficient of the x^2 term twice the coefficient of the x term. Work out the value of k.

(x + 4) (x 2 - kx - 5) = x 3 - kx 2 - 5x + 4x 2 - 4kx - 20 = x 3 + (4-k)x 2 + (-5-4k)x - 20.The coefficients are: (4-k) of x 2 and (-5-4k) of x. Now we can write the equation:(4-k) = 2(-5 - 4k) /expand4 - k ...
MF
10551 Views