-If 7 sin^2A + 3cos^2A = 4, show that tan A=1/√3
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Step-by-step explanation:
use the trigonometric identity
sin^2A+cos^2A=1
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Answered by
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Step-by-step explanation:
7sin^2A+3cos^2A=4
4sin^2A+3sin^2A+3cos^2A=4
4sin^2A+3(sin^2A+cos^2A)=4
4sin^2A+3(1)=4
sin^2A=(4-3)/4
sin^2A=1/4
by taking square root on both sides,
sinA=1/2
cosA=√(1-sin^2A)
cosA=√(1-1/4)
cosA=√3/2
tanA=sinA/cosA
tanA=(1/2)/(√3/2)
tanA=(1/2)*(2/√3)
tanA=1/√3
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