Answer to Question #9700 in Trigonometry for Laurel Mallea

Question

verify each identity
9. cos (θ + (π/2)) = -sinθ
10. (sin (α - β))/(sin α cos β) = 1 - cot α tan β
11 sin t cos t(tan t + cot t) = 1

Answer 1

9.right

10. sin (α - β)=sin α cosβ -cos α sinβ
So& (sin (α - β))/(sin α cos β)=(sin α cosβ -cos α sinβ )/(sin α cos β)=1-cot α tan β

11. sin t cos t(tan t + cot t) = sin t cos t(sin t/cos t + cos t/sin t) =sin^2 t+cos^2 t=1