Prove that cos12π−sin12π=21

cos(12π)−sin(12π)=2[21cos(12π)−21sin(12π)]=2[cos(4π) cos(12π)−sin(4π)sin(12n)]=2cos(4π)+12π=2cos(124π)=2cos(3π)=221=21Hence cos(12π)−sin(12π)=21

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Prove that { }{12}-{ }{12}={1}{{2}}

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Prove that $cos \frac{π}{12} - sin \frac{π}{12} = \frac{1}{2}$

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Prove that

cos \frac{π}{12} - sin \frac{π}{12} = \frac{1}{2}

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cos (\frac{π}{12}) - s in (\frac{π}{12})

= 2 [\frac{1}{2} cos (\frac{π}{12}) - \frac{1}{2} s in (\frac{π}{12})]

= 2 [cos (\frac{π}{4}) cos (\frac{π}{12}) - s in (\frac{π}{4}) s in (\frac{n}{12})]

= 2 cos (\frac{π}{4}) + \frac{π}{12}

= 2 cos (\frac{4 π}{12}) = 2 cos (\frac{π}{3}) = 2 \frac{1}{2} = \frac{1}{2}

Hence

cos (\frac{π}{12}) - s in (\frac{π}{12}) = \frac{1}{2}

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Question Text	Prove that $cos \frac{π}{12} - sin \frac{π}{12} = \frac{1}{2}$
Answer Type	Text solution:1
Upvotes	150