Question

If sin(A-32) cos(A-42), O'SA 90' then the
value of A is​

Answer 1

$\text{I think the question should be:}$

$\textbf{If sin(A-32)=cos(A-42),}\;0<A<90\;\text{then the value of A}$

$\bf\textsf{Given:}$

$\mathsf{sin(A-32)=cos(A-42)}$

$\bf\textsf{To find:}$

$\textsf{The value of A}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{sin(A-32)=cos(A-42)}$

$\textsf{Using,}$

$\boxed{\mathsf{sin\,A=cos(90-A)}}$

$\mathsf{cos(90-(A-32))=cos(A-42)}$

$\mathsf{cos(90-A+32)=cos(A-42)}$

$\mathsf{cos(122-A)=cos(A-42)}$

$\implies\mathsf{122-A=A-42}$

$\implies\mathsf{-2A=-164}$

$\implies\mathsf{A=\dfrac{-164}{-2}}$

$\implies\mathsf{A=82^{\circ}}$

$\bf\textsf{Answer:}$

$\textsf{The value of A is}\;$

$\mathsf{82^{\circ}}$

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