4[sin4 30+cos4 60]-2/3[sin2 60-cos2 45 ] + 1/2 tan2 60
To do this question exact values must be known, that is:
$\displaystyle sin(30) = cos(60) = \frac{1}{2}$
$\displaystyle tan(60) = \sqrt(3)$
$\displaystyle sin(45) = cos(45) = \frac{1}{\sqrt(2)}$
If you did not already know:
$\displaystyle tan(30) = \frac{1}{\sqrt(3)}$
$\displaystyle sin(60) = cos(30) = \frac{\sqrt(3)}{2}$
$\displaystyle tan(45) = 1$
Now, all that is needed is a substitution:
$\displaystyle 4(\frac{1}{2})^4 + 4(\frac{1}{2})^4 - \frac{2}{3}[(\frac{1}{2})^2 - (\frac{1}{\sqrt(2)})^2] + \frac{1}{2}[\sqrt(3)]^2$
and then it should be easy to solve from there
hi thanks for this solutions, and do you have any ideas you can give me for solving my questions. because this is just a try i gave to this place for solutions. This question i had got from my institute pioneermathematics and they have solutions too.
I can't give you ideas for solving other questions if I don't know what the questions are. Are you asking for the final answer to the question? I evaluated it to be 11/6, but I'm sure you could have done it as well