Question

Please help with this question

Answer 1

Answer:

cos(x=pi/4)= $\frac{17}{26}*\sqrt{2}$

Step-by-step explanation:

Remember that $sin^{2}(x) +cos^{2}(x)=1$

We need to find cos(x) from the above equation.

cos(x)= 12) / 13. This solution is positive since cos(x) in the range (2pi/3, 2pi) is positive.

Now, to obtain cos(x+pi/4) lets use the relation for cos(a+b)= cos(a)*cos(b)-sin(a)*sin(b)

where a=x, b =pi/4

Hence

cos(x+pi/4) =cos(x)*cos(pi/4) - sin(x)*sin(pi/4)

cos(x+pi/4) = $\frac{\sqrt{2}}{2} * (cos(x)+5/13)$

cos(x=pi/4)=$\frac{\sqrt{2} }{2} *(\frac{12}{13}+\frac{5}{13})=\frac{17}{26} \sqrt{2}$