Question

Prove that:-

Cos15°-Sin15°=1/underoot2

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Answer 1

Step-by-step explanation:

check whether if in your question in RHS side there is minus one upon root 2 then it is correct ......

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Answer 2

$\huge \underline \mathfrak {Solution:-}$

$\cos(15) - \sin(15) \\ \\ = \cos(45 - 30) - \sin(45 - 30) \\ \\ = \cos(45) \cos(30) + \sin(45) \sin(30) \\ - \sin(45) \cos(30) + \cos(45) \sin(30) \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} - \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} \\ + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = \frac{1}{2 \sqrt{2} } ( \sqrt{3} + 1 - \sqrt{3} + 1) \\ \\ = \frac{1}{2 \sqrt{2} } (2) \\ \\ = \frac{1}{ \sqrt{2} }$

Hence proved