Question

a+b+c=180 and cosa =cosb cosc then prove that cotb cotc=1/2

Answer 1

cosa=cosb cosc

sina/cosa=(sina/cosb cosc)

tana=sin(b+c)/cosb cosc

tana=sinb cosc+cosb sinc/cosb cosc

tana=tanb +tanc


then tan(b+c)=tanb+tanc/1-tanb tanc

-tana = tana/1-tanb tanc

tanb tanc= 2

cotb cotc =1/2 from a+b+c= 180

Answer 2

Answer:

Step-by-step explanation:

cosa=cosb cosc

sina/cosa=(sina/cosb cosc)

tana=sin(b+c)/cosb cosc

tana=sinb cosc+cosb sinc/cosb cosc

tana=tanb +tanc

then tan(b+c)=tanb+tanc/1-tanb tanc

-tana = tana/1-tanb tanc

tanb tanc= 2

cotb cotc =1/2 from a+b+c= 180