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find the expression cot9+cot27+cot63+cot81

find the expression cot9+cot27+cot63+cot81

Grade:11

1 Answers

Shubham Kamleshbhai Patel
59 Points
5 years ago
In this case u need grouping.
 
=> (cot 9° + cot 81°) + (cot 27° + cot 63°)
Convert cot to sin and cos
 
=> [(cos 9° / sin 9°) + (cos 81° / sin 81°)] + [(cos 27° / sin 27°) + (cos 63° / sin 63°)]
 Using cross-multiplication,
=>[(sin 81° . cos 9° + cos 81° . sin 9°)/(sin 9° . sin 81°)] + [(sin 63°. cos 27° + cos 63° . sin 27°)/(sin 27° . sin 63°)]
 
Solving it, u will get the answer as 4√5.

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