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Trigonometrical Ratios of Submultiple of an Angle

An angle of the form A/n where n is an integer is called submultiple angle of A

  1. \displaystyle \left| \sin { \frac { A }{ 2 } } +\cos { \frac { A }{ 2 } } \right| =\displaystyle\sqrt { 1+\sin { A } } or\displaystyle \sin { \frac { A }{ 2 } } +\cos { \frac { A }{ 2 } } =\displaystyle \pm \sqrt { 1+\sin { A } } \displaystyle \left[ +ve,  if\quad 2n\pi -\frac { \pi }{ 4 } \le \frac { A }{ 2 } \le 2n\pi +\frac { 3 }{ 4 } \\ otherwise,-ve\right]
  2. \displaystyle \left| \sin { \frac { A }{ 2 } } -\cos { \frac { A }{ 2 } } \right| =\displaystyle \sqrt { 1-\sin { A } } or \displaystyle \sin { \frac { A }{ 2 } } -\cos { \frac { A }{ 2 } } =\displaystyle \pm \sqrt { 1-\sin { A } }  \displaystyle \left[ +ve,if\quad 2n\pi +\frac { \pi }{ 4 } \le \frac { A }{ 2 } \le 2n\pi +\frac { 5\pi }{ 4 } \\ otherwise,-ve\right]
  3. \displaystyle \tan { \frac { A }{ 2 } } =\displaystyle \frac { \pm \sqrt { { tan }^{ 2 }A+1 } -1 }{ \tan { A } }

 

 

 

February 22, 2019
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Nishant Agrawal

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Introduction to Trigonometry

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