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If A= tan 60 tan 42 and B=cot 60 cot 78,then A= ​ ​

If A= tan 60 tan 42 and B=cot 60 cot 78,then A=

Grade:8

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
Dear student,

Please find the solution below

A=tan6°tan42° and B=cot66°cot78°
A/B=tan6°tan42°tan66°tan78°
Using tan(60-x)tanxtan(60+x)=tan3x for x=18° we get
tan42°tan18°tan78°=tan54°...(1)
for x=6° we get
tan54°tan6°tan66°=tan18°...(2)
Eliminating tan54°between (1) and (2)
we get
tan6°tan42°tan66°tan78°=1
Hence A/B=1.

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