Question

In this triangle, the product of sin b and tan c is , and the product of sin c and tan b is .

Answer 1

Explanation:

by sin formula

sinA/a=sin B/b=sin C/c=k(say)

sin A=ka

sin B=kb

sin C=kc

cos C=√(1-sin²C)=√(1-k²c²)

tan C=kc/√(1-k²c²)

cos B=√(1-sin²B)=√(1-k²b²)

tan B=kb/√(1-k²b²)

sin B × tan C=kb×kc/√(1-k²c²)=(k²bc)/√(1-k²c²)

sin C× tan B=kc×kb/√(1-k²b²)=k²bc/√(1-k²b²)