If =tan6tan42. And b=cot66cot78,. Then find relation between a and b
Akhil , 7 Years ago
Grade 11
Trigonometry> If =tan6tan42. And b=cot66cot78,. Then fi...
1 Answers
Arun
Dear Akhil
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.
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.
Regards
Arun (askIITians forum expert)
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