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3.Trigonometrical Ratios, Functions and Identities
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The expression $[1 - sin (3\pi - \alpha ) + cos (3\pi + \alpha )]$ $\left[ {1\,\, - \,\,\sin \,\left( {\frac{{3\,\pi }}{2}\,\, - \,\,\alpha } \right)\,\, + \,\,\cos \,\left( {\frac{{5\,\pi }}{2}\,\, - \,\,\alpha } \right)} \right]$ when simplified reduces to :
A
$sin \,2\alpha$
B
$- sin\, 2\alpha$
C
$1 - sin\, 2\alpha$
D
$1 + sin\, 2\alpha$
Solution
$[1- sin\alpha – cos\alpha ] \,[ 1 + cos\alpha + sin\alpha ]$
$= 1 – (sin\alpha + cos\alpha )^2 $ $= – sin2\alpha$
Standard 11
Mathematics
