Some Important Results
Category : JEE Main & Advanced
(1)
\[a=h\,(\cot \alpha -\cot \beta )=\frac{h\sin (\beta -\alpha )}{\sin \alpha .\sin \beta }\] \[\therefore \,h=a\sin \alpha \sin \beta \,co\text{sec }(\beta -\alpha )\] and \[d=h\cot \beta =a\sin \alpha .\cos \beta .\text{cosec}(\beta -\alpha )\] |
(2)
\[H=x\cot \alpha \tan (\alpha +\beta )\] |
(3)
\[a=h(\cot \alpha +\cot \beta ),\] where by \[h=a\sin \alpha .\sin \beta .\text{cosec}(\alpha +\beta )\] and \[d=h\cot \beta =a\sin \alpha .\cos \beta .\text{cosec }(\alpha +\beta )\] |
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(4)
\[H=\frac{h\cot \beta }{\cot \alpha }\] |
(5)
\[h=\frac{H\sin (\beta -\alpha )}{\cos \alpha \sin \beta }\] or \[H=\frac{h\cot \alpha }{\cot \alpha -\cot \beta }\] |
(6)
\[H=\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )}\] |
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(7)
\[AB=CD\]. Then, \[x=y\tan \left( \frac{\alpha +\beta }{2} \right)\] |
(8) |
(9)
\[h=\frac{AB}{\sqrt{{{\cot }^{2}}\beta -{{\cot }^{2}}\alpha }}\] |
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(10)
\[h=AP\sin \alpha \] \[=a\sin \alpha .\sin \gamma .c\text{osec}(\beta -\gamma )\] and If \[AQ=d\], then \[d=AP\text{ }\cos \alpha =a\text{ }\cos \alpha .\sin \gamma \text{ }.\text{ cosec }(\beta -\gamma )\] |
(11) |
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