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3.Trigonometrical Ratios, Functions and Identities
hard
The expression,$\frac{{\tan \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)\,\,\,\cos \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)}}{{\cos \,(2\,\pi \,\, - \,\alpha )}}$ $+ cos \left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right) \,sin (\pi -\alpha ) + cos (\pi +\alpha ) sin \,\left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right)$ when simplified reduces to :
A
$0$
B
$1$
C
$-1$
D
none
Solution
$\frac{{ – \,\cot \alpha \,\,\sin \alpha }}{{\cos \alpha }} + sin\alpha . sin\alpha + cos\alpha . cos\alpha = -1+1 = 0$
Standard 11
Mathematics
