Question

find the value of 2cos 22 1/2×cos67 1/2​

Answer 1

$\textbf{Given:}$

$\mathsf{2\;cos\,22\frac{1}{2}^\circ\;cos\,67\frac{1}{2}^\circ}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{2\;cos\,22\frac{1}{2}^\circ\;cos\,67\frac{1}{2}^\circ}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{2\;cos\,22\frac{1}{2}^\circ\;cos\,67\frac{1}{2}^\circ}$

$\mathsf{Using,}$

$\boxed{\mathsf{cos\theta=sin(90^\circ-\theta)}}$

$\mathsf{=2\;cos\,22\frac{1}{2}^\circ\;sin\,22\frac{1}{2}^\circ}$

$\mathsf{Using,}\;\boxed{\bf\;sin2A=2\;sinA\;cosA}$

$\mathsf{=sin2(22\frac{1}{2}^\circ)}$

$\mathsf{=sin\,45^\circ}$

$\mathsf{=\dfrac{1}{\sqrt{2}}}$

$\implies\boxed{\mathsf{2\;cos\,22\frac{1}{2}^\circ\;cos\,67\frac{1}{2}^\circ=\dfrac{1}{\sqrt{2}}}}$

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Answer 2

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