Expand cos(50°) using a double angle identity
To expand cos(50°) using a double angle identity, we can use the formula cos(2θ) = 2cos²(θ) - 1.
In this case, we want to find cos(50°), so we first need to find an angle that is half of 50°.
To find the half angle, we divide 50° by 2:
θ = 50° / 2 = 25°
Now we can substitute this value into the double angle identity formula:
cos(2θ) = 2cos²(θ) - 1
Plugging in θ = 25°, we have:
cos(50°) = 2cos²(25°) - 1
Now we need to find cos²(25°) to complete the expansion. However, instead of doing this manually, we can use a calculator or a trigonometric table to simplify the calculation.
Using a calculator or a trigonometric table, we find that cos(25°) is approximately 0.9063.
Now we can substitute this value into the formula:
cos(50°) = 2(0.9063)² - 1
Simplifying further:
cos(50°) = 2(0.8211) - 1
Finally, we can calculate the answer:
cos(50°) ≈ 0.6422
recall that cos(2x) = 2cos^2(x) - 1
Looks like you just need to review the formulas some ...