Question

cos square 15 - sin square 45 = ​

Answer 1

Step-by-step explanation:

Cos²15-Sin²45

={Cos(45-30)}²-Sin²45

={Cos 45.Cos 30+Sin 45.Sin 30 } ²- {Sin 45}²

=

${(\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} )}^{2} - {( \frac{1}{ \sqrt{2} } )} ^{2}$

${ (\frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} })} ^{2} - \frac{1}{2}$

$( \frac{ \sqrt{3} + 1 }{2 \sqrt{2} }) ^{2} - \frac{1}{2}$

$\frac{3 + 2 \sqrt{3 } + 1 }{8} - \frac{1}{2}$

$\frac{4 + 2 \sqrt{3} - 4}{8}$

$\frac{2 \sqrt{3} }{8}$

$\frac{ \sqrt{3} }{4}$

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Answer 2

Answer:

Answer is sin 420°,cos 390°