Question

Find the value of sin 75° + cos 75° ?​

Answer 1

Answer:

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$\sin75 + \cos75 = \sin75 + \cos(90 - 15)$

$= \sin75 + \sin15$

$= 2 \sin( \frac{75 + 15}{2} ) \cos( \frac{75 - 15}{2} )$

$= 2 \sin45 \cos30$

$= 2 \times \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2}$

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

Answer 2

Step-by-step explanation:

$\sin(75) + \cos(75) = \sin(75) + \cos(90 - 15)$

$= \sin(75) + \sin(15)$

$= 2 \sin( \frac{75 + 15}{2} ) \cos( \frac{75 - 15}{2} )$

$= 2 \sin(45) \cos(30)$

$2 \times \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2}$

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