If $tan\ 80^o = a$ and $tan47^o = b$, then $tan37^o$ is equal to -
If $tan\ 80^o = a$ and $tan47^o = b$, then $tan37^o$ is equal to -
- A
$\frac{{\alpha \, - \,\beta }}{{1\, + \,\alpha \beta }}$
- B
$\frac{{\alpha \beta \, + \,1}}{{\alpha \, - \,\beta }}$
- C
$\frac{{\alpha \beta \, - \,1}}{{\alpha \, + \,\beta }}$
- D
$\frac{{\alpha \, + \,\beta }}{{1\, - \,\alpha \beta }}$
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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 :
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 :