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3.Trigonometrical Ratios, Functions and Identities
easy
જો $x + y + z = {180^o},$ તો $\cos 2x + \cos 2y - \cos 2z = . . . .$
A
$4\sin x.\,\sin y.\,\sin z$
B
$1 - 4\sin x.\,\sin y.\,\cos z$
C
$4 sin x. sin y. sin z -1$
D
$\cos A.\cos B.\cos C$
Solution
(b) $\cos 2x + \cos 2y – \cos 2z$
$ = 2\cos (x + y)\cos (x – y) – 2{\cos ^2}z + 1$
$ = 2\cos (\pi – z)\cos (x – y) – 2{\cos ^2}z + 1$
$ = 1 – 2\cos z\{ \cos (x – y) – \cos (x + y)\} $
$ = 1 – 2\cos z2\sin x\sin y = 1 – 4\sin x\sin y\cos z$.
Standard 11
Mathematics
