Question

if [-2/3 5/2] = x/3. 5/y] then principal value of cos-1 (y/2x) is:​

Answer 1

Answer:

1/2 (3-√5) is a right answer

Answer 2

Answer:

The principle value is  $\frac{2\pi }{3}$.

Step-by-step explanation:

Given that [-2/3,5/2] = [x/3,5/y]

We have to find the principal value of $cos^{-1} (\frac{y}{2x} )$

Given [-2/3,5/2] = [x/3,5/y]

Comparing the terms, then

$\frac{-2}{3} =\frac{x}{3}$

-2 = x.

And $\frac{5}{2} =\frac{5}{y}$

$\frac{1}{2} =\frac{1}{y}$

y = 2

Now we find the value of  $cos^{-1} (\frac{y}{2x} )$

Let y = $cos^{-1} (\frac{y}{2x} )$ = $cos^{-1} (\frac{2}{2(-2)} ) = cos^{-1} (\frac{1}{-2} )= cos^{-1}(-\frac{1}{2} )$

$y = cos^{-1} (-\frac{1}{2} )\\cos(y) = -\frac{1}{2} \\cos(y) = cos(\frac{2\pi }{3} )$

Therefore, the principle value is $\frac{2\pi }{3}$