00:00Given here in the equation, x square minus 2x cos theta plus 1 is equal to 0, we get x
00:05If the value of has been asked, then it is a quadratic equation, its root has to be found, so basically we will apply the formula,
00:13root x is equal to minus b, b is what you have, b is the minus of 2x, minus
00:212 cos theta, that is, minus 2 cos theta, then it becomes 2 cos
00:27theta, the formula is, x is equal to minus b plus minus, under root b square minus 4, such that
00:36I have 2,
00:36What you get is this, 1, which means it's going to be divided down, this 2a, which means 2 into 1, 2, 2
00:46divided by down, so 2 cos theta, plus minus, under root, b square, b, minus 2 cos theta
00:56, then b squared is
00:574 cos square theta, minus 2, that is, minus 4 into 1, that is, minus 4, now that's 4
01:07Taking common, this becomes, x is equal to 2 cos theta, plus minus 4 taking common,
01:15Then the 4 is taken out once, so it becomes,
01:182 under root, cos square theta, minus 1, now 2 in one, this 2 is common to this 2
01:28So, x is equal to cos theta, plus minus, under root, cos square theta, minus 1,
01:36What can we write for 1, sin is square theta, plus cos square theta, that is, minus, sin is square
01:44theta, minus cos square theta, will be multiplied by minus 1 on both, that will be minus multiplied,
01:51So cos square theta, minus cos square theta, zero, that means it comes to, cos theta, plus minus, under root
01:59in, minus cos square theta, this is minus sin square theta,
02:05sin square theta, so if I write it in complex number form, it becomes, x is equal to
02:14cos theta, plus, plus iota sin theta,
02:21a root this, and a cos theta, minus iota sin theta, so the magnitude in Fib times we know what
02:28will go,
02:29under root, a plus iota also, so under root, a square plus b square, i.e. magnitude, under root cos
02:37square theta, plus sin square theta,
02:40cos square theta, plus sin square theta, magnitude of x is complex number, the formula for the magnitude of complex number is
02:48would have been, direct,
02:49its square square plus its square, so this is the identity, under root is 1, which means the answer is 1.
02:56Khidāib.
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