Question

if cotAcotB=2

show that cos(A+B)/cos(A-B)=1/3

Answer 1

Given:- cotA*cotB=2

To Prove:- cos(A+B)/cos(A-B)=1/2

Solution:- ● cos(A+B)/cos(A-B)

● cosAcosB -

sinAsinB/cosAcosB+sinAsinB

● cotAcotB-1/cotAcotB+1

● 2-1/2+1 [since,cotAcotB=2(given)]

●so,1/3

*Hence Proved*

THANK YOU

Answer 2

HELLO DEAR,

GIVEN:- cotA × cotB = 2

now, cos(A + B)/cos(A - B)

=> cosAcosB - sinAsinB/cosAcosB + sinAsinB

[diving both in num. & deno. by sinAsinB]

=> cotAcotB - 1/cotAcotB + 1

[cotAcotB = 2]

=> 2 - 1/2 + 1

=> 1/3

hence, cos(A + B)/cos(A - B) = 1/3

I HOPE IT'S HELP YOU DEAR

THANKS