Use the following to answer questions :
-Use a half-angle identity to find the exact value of cos$\theta$.

Question

Use the following to answer questions : 
-Use a half-angle identity to find the exact value of cos$\theta$.

Quizplus · Accepted Answer

Using the half-angle identity, we have:

cos(F/2) = ±sqrt[(1 + cosF)/2]

Since F = 2θ, we have:

cos(θ) = cos(F/2) = ±sqrt[(1 + cosF)/2]

Taking the positive sign because θ lies in the first quadrant, we get:

cos(θ) = sqrt[(1 + cosF)/2]

Solving for cosF, we have:

cosF = 2cos^2(θ) - 1

Substituting θ = π/12, we get:

cosF1F1F1S1F1F1F10 = 2cos^2(π/12) - 1 = 11ea7f29_4ffb_ccac_9ecd_290072ddaa0f_TB3307_11

Use the Following to Answer Questions : -Use a Half-Angle