- Home
- Standard 11
- Mathematics
$\frac{{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi \over 2}}} \right)\,\,.\,\,\cos \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)\,\, - \,\,{{\sin }^3}\,\left( {{\textstyle{{7\pi } \over 2}}\,\, - \,\,x} \right)}}{{\cos \,\,\left( {x\,\, - \,\,{\textstyle{\pi \over 2}}} \right)\,\,.\,\,\tan \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)}}$ when simplified reduces to :
$sin \,x\, cos\, x$
$- sin^2\, x$
$- sin\, x\, cos\, x$
$sin^2x$
Solution
$\frac{{\tan \,\,\left( {x\,\, – \,\,{\textstyle{\pi \over 2}}} \right)\,\,.\,\,\cos \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)\,\, – \,\,{{\sin }^3}\,\left( {{\textstyle{{7\pi } \over 2}}\,\, – \,\,x} \right)}}{{\cos \,\,\left( {x\,\, – \,\,{\textstyle{\pi \over 2}}} \right)\,\,.\,\,\tan \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)}}$
$=$$\frac{{ – \cot x\,.\,\sin x\, + \,{{\cos }^3}x}}{{ – \sin x\,.\cot x}}$ $=$$\frac{{{{\cos }^3}x\, – \,\frac{{\sin x.\cos x}}{{\sin x}}}}{{ – \,\sin x\,.\,\frac{{\cos x}}{{\sin x}}}}$ $= sin^2x$
