If then prove that tanA = 1/√3

1.	If then prove that tanA = 1/√3
Answer» To PROVE :- $\sf{tanA=\frac{1}{\sqrt{3}}}$ PROOF :- GIVEN, $\sf{7sin^2A+3cos^2A=4}$ _________ $\sf{7sin^2A+3cos^2A=4}$ $:\implies\sf{7sin^2A+3(1-sin^2A)=4}$ $:\implies\sf{7sin^2A+3-3sin^2A=4}$ $:\implies\sf{4sin^2A=1}$ $:\implies\sf{sin^2A=\frac{1}{4}}$ $:\implies\sf{sinA=\sqrt{\frac{1}{4}}=\frac{1}{2}}$ $:\implies\sf{sinA=sin30^{\circ}}$ $:\implies\sf{A=30^{\circ}}$ $\therefore\sf{tanA=tan30^{\circ}=\frac{1}{\sqrt{3}}}$ HENCE,PROVED __________________________________

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