Question

asecA+bsecB+csecC=a secA tanB tanC
Proof this please

Answer 1

Step-by-step explanation:

we know that

A+B+C=180*

A+B =180*-C

tan(A+B)=tan(180*-c)

tanA+tanB

------------------=-tanC

1-tanAtanB

tanA+tanB=-tanc(1-tanAtanB)

tanA+tanB=-tanC+tanAtanBtanc

tanA+tanB+tanC=tanAtanBtanC

sinA sinB sinC sinA sinB sinC

-------+---------+--------=------- ------- --------

cosA cosB cosC cosA cosB cosC

a b c a/k sinB sinC

------- +-------- +--------- =----- ---------- --------

k cosA kcosB cosc cosA cosB cosC

asecA+bsecB+csecC=asecA tanB tanC