Question

If cos (A - B) =3/5
and tan A tan B = 2, then prove that :
COS A cos B =1/5
​

Answer 1

$\huge\mathbb\color{teal}ANSWER:-$

$Cos(A - B)=\frac{3}{5}$

$CosA*CosB+SinA*SinB =\frac{3}{5}$-(1)

$tanA*tanB = 2$

$SinA*SinB = 2CosA*CosB$-(2)

$From \: eq.(1) + eq.(2)-$

$CosA*CosB + 2CosA*CosB =\frac{3}{5}$

$3CosA*CosB =\frac{3}{5}$

$CosA*CosB =\frac{1}{5}$