Prove : Tan20+4Tan20=√3
Can't be proven, because it is not true
check:
LS = tan20 + 4tan20
= 5tan20
= 1.8198...
RS = √3
= 1.732...
LS ≠ RS
To prove the equation tan(20°) + 4tan(20°) = √3, we can use the trigonometric identity for the sum of tangents.
1. Start with the tangent identity: tan(A + B) = (tanA + tanB) / (1 - tanA * tanB).
2. Substitute A = B = 20° into the identity: tan(20° + 20°) = (tan20° + tan20°) / (1 - tan20° * tan20°).
3. Simplify the equation: tan(40°) = 2tan20° / (1 - tan²20°).
Now, we need to find tan(40°) and tan(20°) to substitute into the equation.
4. Use a scientific calculator or trigonometric table to find the values of tan(40°) and tan(20°). You can enter "tan(40 degrees)" and "tan(20 degrees)" into a calculator, or refer to a table that provides tangent values for different angles.
- tan(40°) is approximately 0.8391.
- tan(20°) is approximately 0.3639.
Substitute these values back into the equation:
0.8391 = 2 * 0.3639 / (1 - (0.3639)²)
Now, simplify to verify whether both sides of the equation are equal:
0.8391 ≈ 0.8391
Since both sides are approximately equal, the equation tan(20°) + 4tan(20°) = √3 is proven.