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Prove that tan 6°.tan 42°.tan 66°.tan 78°=1 |
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Answer» Thanx mam 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° = 1HenceL.H.S=R.H.S |
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