If √3 tan A= 3 sin A,prove that sin^2A-cos^2A=1/3
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given,
√3tan A= 3sin A
to prove sin^2A + cos^2A = 1/3
proof,
L.H.S = √3*sinA/cosA = 3sinA
= √3/cosA =3
=cosA= 1/√3.............(1)
in figure,
sinA= √2/√3
cosA=1/√3.
R.H.S =sin^2A -cos^2A
=(√2/√3)^2 - (1/√3)^2
=2/3 - 1/3
=1/3
Hence proved
√3tan A= 3sin A
to prove sin^2A + cos^2A = 1/3
proof,
L.H.S = √3*sinA/cosA = 3sinA
= √3/cosA =3
=cosA= 1/√3.............(1)
in figure,
sinA= √2/√3
cosA=1/√3.
R.H.S =sin^2A -cos^2A
=(√2/√3)^2 - (1/√3)^2
=2/3 - 1/3
=1/3
Hence proved
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