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what is cos(75°)cos(15°) =

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[tex]\dfrac 14[/tex]

Step by step explanation:

[tex]~~~\cos (75^{\circ}) \cos (15^ \circ)\\\\=\dfrac 12 \cdot 2 \cos ( 75 ^\circ}) \cos( 15^\circ})\\\\[/tex]

[tex]=\dfrac 12 \left[\cos \left( 75^ \circ + 15^ \circ \right) + \cos \left( 75^{\circ} - 15^{\circ} \right)\right]~~~~~~;[2 \cos a \cos b = \cos( a+b) + \cos(a-b)]\\[/tex]

[tex]\\=\dfrac 12 \left( \cos 90^{\circ} + \cos 60^{\circ} \right)\\\\=\dfrac 12 \left(0+\dfrac 12 \right)\\\\=\dfrac 12 \cdot \dfrac 12\\\\=\dfrac 14[/tex]
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