Question # WE (EtVGIL
If A = tan 6° tan 42° and B = cot 66° cot 78°,
then -
(A) A = 2B (B) A = B
(C) A = B
(D) 3A = 2B
nen
2.9
Leta B be such that a

# WE (EtVGIL
If A = tan 6° tan 42° and B = cot 66° cot 78°,
then -
(A) A = 2B (B) A = B
(C) A = B
(D) 3A = 2B
nen
2.9
Leta B be such that a

Solution ( A=tan 6^{circ} tan 42^{circ} ) and ( B=cot 66^{circ} cot 78^{circ} )
( mathrm{A} / mathrm{B}=tan 6^{circ} tan 42^{circ} tan 66^{circ} tan 78^{circ} )
Using ( tan (60-x) tan x tan (60+x)=tan 3 x ) for ( x=18^{circ} ) we
get ( tan 42^{circ} tan 18^{circ} tan 78^{circ}=tan 54^{circ} ldots .(1) )
for ( x=6^{circ} ) we get
( tan 54^{circ} tan 6^{circ} tan 66^{circ}=tan 18^{circ} ldots(2) )
Eliminating tan54 'between (1) and (2)
we get
( tan 6^{circ} tan 42^{circ} tan 66^{circ} tan 78^{circ}=1 )
Hence ( mathrm{A} / mathrm{B}=1 )

Solution