Question

If angle A and angle B are acute angles of a right angled triangle ABC , then write the relations between :
(i) sin A and cos B .
(ii ) cos A and sin B

Answer 1

Dear student
$$\begin{gathered} In△ABC,\angle C=90°and\angle Aand\angle Bareacuteangleandbyanglesumpropertyoftriangle, \\ \angle A+\angle B+\angle C=180° \\ \Rightarrow \angle A+\angle B+90°=180° \\ \Rightarrow \angle A+\angle B=90° \\ \Rightarrow \angle A=90°-\angle B \\ Now, \\ 1)\sin A=\sin \left(90°-B\right)=\cos B \\ \Rightarrow \sin A=\cos B \\ 2)\cos A=\cos \left(90°-B\right)=\sin B \\ \Rightarrow \cos A=\sin B \end{gathered}$$
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