Question

Find the value of 2 tan 300 1−tan2300

Answer 1

CORRECTED QUESTION

• Find the value of 2 tan 30° / 1 − tan²30°

Step-by-step explanation:

2 tan 30° / 1 − tan²30°

$\bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty$

2 × 1/√3 / [1 - (1/√3)²]

2/√3 / [1 - 1/3]

2/√3 / [(3 - 1)/3]

2/√3 / 2/3

2/√3 × 3/2

3/√3

√3 or tan 60°

Answer 2

Step-by-step explanation:

1

To Prove: tan(2×300)=1−tan23002tan300

L.H.S: tan(2×30∘)=tan60∘=3

R.H.S: 1−tan23002tan300

= 1−(31)22(31)

= 3232

= 3

Thus, L.H.S=R.H.S