Question

if cos(A-B)=3/5 and tanAtanB=2 then
prove that:-
cosAcosB=1/5

Answer 1

$\huge\textbf{Solution}$
$<b>$
tanA.tanB =2

(SinA/cosA)×(sinB/cosB)=2

or sinA.sinB=2cosA.cosB………………(1)

cos(A-B=3/5

cosA.cosB+sinA.sinB =3/5

On putting sinA.sinB=2cosA.cosB from eq.(1)

cosA.cosB+2cosA.cosB =3/5

cosA.cosB=3/5÷3=1/5…………………….(2)

On putting cosA.cosB=1/5 in eq.(1)

sinA.sinB =2/5……………………(3)

To prove :- cos(A+B) = -1/5

L.H.S.

=cosA.cosB-sinA.zinB

= 1/5–2/5

= -1/5 proved.


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