Question

if 3 tana tan b = 1 , prove that 2 cos( a+b) = cos (a-b)​

Answer 1

Step-by-step explanation:

WE KNOW THAT TAN CHANGES TO COS THEN ......

3TAN B 01, 2COS(A+B)=(A-B)

3COS B O1,2COS(A+B)=(A-B)

A+B=A-B

HENCE PROVES

Answer 2

solution

==>

we have,

3 tana tanB = 1

3 sin a sin b / cosa cosB = 1

sin a sin b/ cos a cos b = 3/1

cos a cos b / sina SinB = 1/3

applying componendo- dividendo

cos a cos b + sinA sinb / cos a cos b - sin a sin b = 1+3 /1-3

cos ( a-b)/cos ( a+b) = 4/ 2

cos ( a-b) = 2 cos ( a+b)

hence proved