Prove that tan 6°.tan 42°.tan 66°.tan …
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Posted by Subhasundar Baishya 5 years, 10 months ago
- 2 answers
Yogita Ingle 5 years, 10 months ago
L.H.S=tan 6 ° tan 42 ° tan 66 ° tan 78 °
now ,
Use Trigonometric Identity
tanx * tan(60° - x) * tan(60° + x) = tan(3x)
set x = 6
tan6° tan54° tan66° = tan18° .................... ((1))
Similarly, set x = 18°
tan18° tan42° tan78° = tan54° ...................... ((2))
((1)) * ((2)):
tan6° * tan54° * tan66° * tan18° * tan42° * tan78° = tan18° * tan54°
tan6° * tan66° * tan42° * tan78° = 1
Hence
L.H.S=R.H.S
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Vansh Prajapati 5 years, 10 months ago
0Thank You