"त्रिकोणमितीय फलन": अवतरणों में अंतर

पंक्ति 121:
|-class="hintergrundfarbe6"
!  
! ज्या
! sin
! कोज्या
! cos
! स्पज्या
! tan
! cot
! कोटिज्या
! sec
! व्युत्क्रम ज्या
! csc
|- align=center
!class="hintergrundfarbe8"| sin(x)
| <math> \,\sin(x) </math>
| <math> \sqrt{1-\cos^2(x)} </math>
| <math> \frac{\tan(x)}{\sqrt{1 + \tan^2(x)}} </math>
| <math> \frac{1}{\sqrt{\cot^2(x) + 1}} </math>
| <math> \frac{\sqrt{\sec^2(x)-1}} {\sec(x)} </math>
| <math> \frac{1}{\csc(x)} </math>
|- align=center
!class="hintergrundfarbe8"| cos(x)
| <math> \, \sqrt{1-\sin^2(x)} </math>
| <math> \, \cos(x) </math>
| <math> \, \frac{1}{\sqrt{1 + \tan^2(x)}} </math>
| <math> \, \frac{\cot(x)} {\sqrt{\cot^2(x)+ 1}} </math>
| <math> \, \frac{1}{\sec(x)} </math>
| <math> \, \frac{\sqrt{\csc^2(x)-1}}{\csc(x)} </math>
|- align=center
!class="hintergrundfarbe8"| tan(x)
| <math> \, \frac{\sin(x)}{\sqrt{1-\sin^2(x)}} </math>
| <math> \, \frac{\sqrt{1-\cos^2(x)}}{\cos(x)} </math>
| <math> \, \tan(x) </math>
| <math> \, \frac{1}{\cot(x)} </math>
| <math> \, \sqrt{\sec^2(x)-1} </math>
| <math> \, \frac{1}{ \sqrt{\csc^2(x)-1}} </math>
|- align=center
!class="hintergrundfarbe8"| cot(x)
| <math> \, \frac{\sqrt{1-\sin^2(x)}}{\sin(x)} </math>
| <math> \, \frac{\cos(x)}{\sqrt{1-\cos^2(x)}} </math>
| <math> \, \frac{1}{\tan(x)} </math>
| <math> \, \cot(x) </math>
| <math> \, \frac{1}{\sqrt{\sec^2(x)-1}} </math>
| <math> \, \sqrt{\csc^2(x)-1} </math>
|- align=center
!class="hintergrundfarbe8"| sec(x)
| <math> \, \frac{1}{\sqrt{1-\sin^2(x)}} </math>
| <math> \, \frac{1}{\cos(x)} </math>
| <math> \, \sqrt{1 + \tan^2(x)} </math>
| <math> \, \frac{\sqrt{\cot^2(x) + 1}}{\cot(x)} </math>
| <math> \, \sec(x) </math>
| <math> \, \frac{\csc(x)}{\sqrt{\csc^2(x)-1}} </math>
|- align=center
!class="hintergrundfarbe8"| csc(x)
| <math> \, \frac{1}{\sin(x)} </math>
| <math> \, \frac{1}{\sqrt{1 - \cos^2(x)}} </math>
| <math> \, \frac{\sqrt{1 + \tan^2 (x)}} {\tan(x)} </math>
| <math> \, \sqrt{\cot^2(x) + 1} </math>
| <math> \, \frac{\sec(x)}{\sqrt{\sec^2(x) - 1}} </math>
| <math> \, \csc(x) </math>
|}