Question

If $1+{\sin }^{2}A=3\sin A\times cosA$ , then what is the value of tan A.

• A. $\frac{1}{2},1$
• B. $\frac{1}{4},2$
• C. $\frac{1}{6},3$
• D. $\frac{1}{8},4$

Answer 1

The correct option is A $\frac{1}{2},1$

$1+{\sin }^{2}A=3\sin A\cos A$

$2{\sin }^{2}A+{\cos }^{2}A=2\sin A\cos A+\sin A\cos A\dots (1=co{s}^{2}A+si{n}^{2}A)$

$2{\sin }^{2}A-2\sin A\cos A=\sin A\cos A-{\cos }^{2}A$

$2\sin A(\sin A-\cos A)-\cos A(\sin A-\cos A)=0$

$(2\sin A-\cos A)(\sin A-\cos A)=0$

$2\sin A-\cos A=0\sin A-\cos A=0$

$\therefore \tan A=\frac{1}{2}\therefore \tan A=1$