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CosecA=P+Q then, cot(A/2+pi/4)=

CosecA=P+Q
then, cot(A/2+pi/4)=

Grade:11

2 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Solution:
We know that:
cosec\left ( A \right )=\frac{1+cot^{2}\left ( \frac{A}{2} \right )}{2cot\left ( \frac{A}{2} \right )}
This yields:
cos\left ( A \right )=\frac{2cot\left ( \frac{A}{2}+\frac{\pi }{4} \right )}{1+cot^{2}\left ( \frac{A}{2}+ +\frac{\pi }{4}\right )}
Hence, using the quadratic equation, we get:
cot\left ( \frac{A}{2}+\frac{\pi }{4} \right )=1\pm \left ( \frac{1}{P+Q} \right )
Thanks & Regards
Sumit Majumdar,
askIITians Faculty
Ph.D,IIT Delhi
Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Dear student,
Please use the half angle formula to get the result:
cosec A=\frac{1+cot^{2}\left ( \frac{A}{2} \right )}{2cot\left ( \frac{A}{2} \right )}
Regards
Sumit

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