Question

cos^2 76° + cos^2 16 - cos 76° cos 16° =
1) 1 12
2) 0

Answer 1

Answer:

$\frac{3}{4}$

Step-by-step explanation:

${ \cos(76) }^{2} + { \cos(16) }^{2} - \cos(76) \cos(16) \\ we \: know \: that \\ {(a - b)}^{2} + ab = {a}^{2} + {b}^{2} - ab \\ so \\ {( \cos(76) - \cos(16)) }^{2} + \cos(76) \cos(16) \\ we \: know \: that \\ \cos(16 + 60) = \cos(60) \cos(16) - \sin(60) \sin(16) \\ \cos(76) = \frac{ \cos(16) }{2} - \frac{ \sqrt{3} \sin(16) }{2} \\ putting \: the \: value \: of \: \cos(76) \\ in \: above \: equation \: \\ {(\cos( \frac{16}{2} ) - \frac{ \sqrt{3} \sin(16) }{2} - \cos(16)) }^{2} + { \frac{ \cos(16) }{2} }^{2} - \frac{ \sqrt{3} \cos(16) \sin(16) }{2} \\ {(\cos( \frac{16}{2} ) + \frac{ \sqrt{3} \sin(16) }{2} })^{2} \: + \frac{ { \cos(16) }^{2} }{2} - \frac{ \sqrt{3} \cos(16) \sin(16) }{2} \\ { \frac{ \cos(16) }{4} }^{2} + \frac{ { 3\sin(16) }^{2} }{4} + \frac{ \sqrt{3} \cos(16) \sin(16) }{2} + \frac{ { \cos(16) }^{2} }{2} - \frac{ \sqrt{3} \cos(16) \sin(16) }{2} \\ \frac{ { 3\cos(16) }^{2} }{4} + \frac{3 \sin(16) }{4} \\ \frac{3}{4} ( { \cos(16) }^{2} + { \sin(16) }^{2} ) \\ \frac{3}{4}$

solutions is attached above too ..