Question

Explain how to find tan θ if sec θ =√(42)/6 and sin θ < 0. What are the half-angle identities? How do the sum and difference formulas for sine differ from cosine?

Answer 1

Explanation:

`sec^2\theta-tan^2 \theta=1\\(42)/(36) -tan^2\theta=1\\tan^2 \theta=(42)/(36)-1=(6)/(36)\\as~ sec~ \theta ~is~positive~and ~sin~\theta~is ~negative.\\\theta~lies~in~4th~quadrant.\\tan~\theta~is~negative.\\tan~\theta=(1)/(√(6) )`