Question

Sa se calculeze sin de 75 grade + cos de 15 grade

Answer 1

= sin 75 + sin(90-15) = 2sin 75 = 2sin (30+45) = 2*2 sin 30 * cos 45 = 4*1/2*rad2 / 2= rad2

Answer 2

[tex]\it E = sin75^0 +cos15^0 \\ \\ sin75^0 = cos(90^0-75^0) = cos15^0\ \ \ (*) \\ \\ (*) \Rightarrow\ E = cos15^0+cos15^0 = 2cos15^0 = 2cos(45^0-30^0) = \\ \\ = 2(cos45^0cos30^0+ sin45^0sin30^0) = 2\left(\dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\right) =[/tex]

$\it= 2\cdot\dfrac{1}{4} (\sqrt6 + \sqrt2) = \dfrac{\sqrt6+\sqrt2}{2}$