Evaluate Cos 45o Cos 30o – Sin 45o Sin 30o leaving the answer in surd form
-
A.
(frac{sqrt{2}-1}{2}) -
B.
(frac{sqrt{3}-sqrt{2}}{4}) -
C.
(frac{sqrt{6}-sqrt{2}}{2}) -
D.
(frac{sqrt{6}-sqrt{2}}{4})
Correct Answer: Option D
Explanation
(cos45^o times cos30^o – sin45^o times sin30^o\
frac{1}{sqrt{2}}times frac{sqrt{3}}{2} – frac{1}{sqrt{2}}times frac{1}{2}\
frac{sqrt{3}}{2sqrt{2}}-frac{1}{2sqrt{2}}; = frac{sqrt{3}-1}{2sqrt{2}}=frac{sqrt{6}-sqrt{2}}{4})