# Answer on Trigonometry Question for Laurel Mallea

Question #9700

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

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

Expert's answer

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

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

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