Tan20+4sin20=√3
Ahhh, you changed it
LS = sin20/cos20 + 4sin20
= sin20/cos20 + 4sin20cos20/cos20
= (sin20 + 4sin20cos20)/cos20
= (sin 20 + 2sin40)/cos20
= (sin20 + 2sin(60-20))/cos20
= (sin20 + 2sin60cos20 - 2cos60sin20)/cos20
= (sin20 + √3 cos20 - sin20)/cos20
= √3cos20/cos20
= √3
Reiny already showed you that this can not be true.
http://www.jiskha.com/display.cgi?id=1442757482
To verify if the equation tan20 + 4sin20 equals √3, we can use a scientific calculator to find the approximate values of tan(20) and sin(20), and then substitute them into the equation. If they indeed result in the square root of 3, then the equation is satisfied.
Let's break down the steps to finding the approximate values of tan(20) and sin(20) on a scientific calculator:
1. Ensure that your calculator is set to the desired angle unit. In this case, we will use degrees.
2. Enter the value 20 on the calculator.
3. Find the tangent of 20 degrees (tan(20)) by pressing the "tan" button on your calculator. The result might be a decimal number.
4. Next, find the sine of 20 degrees (sin(20)) by pressing the "sin" button on your calculator. This will also result in a decimal number.
5. Now, substitute the approximate values of tan(20) and sin(20) into the equation: tan20 + 4sin20 = √3.
Let's denote the approximate value of tan(20) as "a" and sin(20) as "b".
The equation can then be rewritten as: a + 4b = √3.
6. Calculate the left side of the equation by substituting "a" and "b" with the decimal values you obtained in step 4.
Let's say the calculated value of a is 0.3639 and b is 0.3420.
The equation becomes: 0.3639 + 4 * 0.3420 = √3
7. Evaluate the left side of the equation: 0.3639 + 1.368 = √3
Simplifying further, we get: 1.7319 = √3
8. Finally, calculate the approximate value of √3 using a calculator, and check if it matches the value obtained in step 7.
On most calculators, the square root operation is represented by the √ button.
The value of √3 is approximately 1.732.
Since 1.7319 is very close to 1.732, we can conclude that tan20 + 4sin20 is approximately equal to √3.
This calculation method should help you solve the equation and check if the given equation is satisfied.