.If tan A = 1\√3and tan B = 3, then show that cos A cos B – sin A sin B = 0.
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tan A = 1/root 3 tan B = 3/1
P=1 ,B = Root3 P= 3 B= 1
1^2 + (root3)^2= H^2 3^2+1^2=H^2
1+ 3 = H^2 9+ 1 =H^2
4 = H^2 10 =H^2
H= 2 H=ROOT 10
so ,
SIN A = P/H = 1/2
SIN B = P/H= 3/Root10
COS A = B/H = root3/2
COS B = B/H = 1/root 10
cosACOSB -SINASINB= 0
(root3/2) .( 1/Root10) -(1/2).(3/root10)=0
they will cancel to each other and ans will be
0= 0
HOPE THIS ANS WILL HELP YOU .
P=1 ,B = Root3 P= 3 B= 1
1^2 + (root3)^2= H^2 3^2+1^2=H^2
1+ 3 = H^2 9+ 1 =H^2
4 = H^2 10 =H^2
H= 2 H=ROOT 10
so ,
SIN A = P/H = 1/2
SIN B = P/H= 3/Root10
COS A = B/H = root3/2
COS B = B/H = 1/root 10
cosACOSB -SINASINB= 0
(root3/2) .( 1/Root10) -(1/2).(3/root10)=0
they will cancel to each other and ans will be
0= 0
HOPE THIS ANS WILL HELP YOU .
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