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  • The value of <img alt="\sin 23^{\circ}\: \cos 67^{\circ}+\cos 23^{\circ}\: \sin 67^{\circ}is" src="https://learn.careers360.com/latex-image/?%5Csin%2023%5E%7B%5Ccirc%7D%5C%3A%20%5Ccos%2067%5E%7B%5Ccirc%7D&plus;%5Ccos%2023%5E%7B%5Ccirc%7D%5C%3A%20%5

The value of \sin 23^{\circ}\: \cos 67^{\circ}+\cos 23^{\circ}\: \sin 67^{\circ}is__________

 

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\sin 23^{\circ}\: \cos 67^{\circ}+\cos 23^{\circ}\: \sin 67^{\circ} \\\\ = \sin 23^{\circ}\: \cos (90-23)^{\circ}+\cos 23^{\circ}\: \sin (90-23)^{\circ} \\=\sin 23^{\circ}\: \sin 23^{\circ}+\cos 23^{\circ}\: \cos 23^{\circ} \\ =\sin^2 23^{\circ}+\cos^2 23^{\circ} \\=1 \\

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