1
Question
In a triangle ABC, which is not right angled, then ∑ cos A.cos B.cosec C =___
In a triangle ABC, which is not right angled, then ∑ cos A.cos B.cosec C =___
Open in App
Solution
The correct option is B 2
∑cosAcosecBcosecC=∑cosAsinBsinC=−∑cos(B+c)sinBsinc[InΔABC,A+B+C=π]=−∑cosBcosC−sinBsinCsinBsinC=∑(1−cotAcotB)=∑1−∑cotAcotB
=3-1
=2
{In ΔABC cot A cot B +cot B cot C +cot C cot A=}
∑cosAcosecBcosecC=∑cosAsinBsinC=−∑cos(B+c)sinBsinc[InΔABC,A+B+C=π]=−∑cosBcosC−sinBsinCsinBsinC=∑(1−cotAcotB)=∑1−∑cotAcotB
=3-1
=2
{In ΔABC cot A cot B +cot B cot C +cot C cot A=}
Suggest Corrections
16
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
