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In a right triangle, one angle measures x∘x^\circ, where\newlinesin⁡x∘=45\sin x^\circ = \frac{4}{5}. What is cos⁡(90∘−x∘)\cos(90^\circ - x^\circ) ?

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Q. In a right triangle, one angle measures x∘x^\circ, where\newlinesin⁡x∘=45\sin x^\circ = \frac{4}{5}. What is cos⁡(90∘−x∘)\cos(90^\circ - x^\circ) ?
  1. Identify Relationship: Identify the relationship between sine and cosine in complementary angles.\newlineUsing the identity cos⁡(θ)=sin⁡(90°−θ)\cos(\theta) = \sin(90° − \theta), we can find cos⁡(90°−x°)\cos(90° − x°) by calculating sin⁡x°\sin x°.\newlinesin⁡x°=45\sin x° = \frac{4}{5}, so cos⁡(90°−x°)=sin⁡x°=45\cos(90° − x°) = \sin x° = \frac{4}{5}.

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