Can someone please help me with my Homework?

Question

Whoever can help me out gets 10 points!


Pie= sign of pie theta= sign theta


Prove the following equation:

tan((pie/40+(theta/2))=1cos(theta)+sin(theta) /1+cos(theta)-sin(theta)


Suppose that x+ (1/x) = 2cos(theta)

Show that x^2 +(1/x^2)=2cos(2theta)

Answer 1

tan(pie/4 +theta/2)
= (tan(pie/4) + tan(theta/2)) / (1 - tan(pie/4)*tan(theta/2))
= (1+tan(theta/2)) / (1-tan(theta/2))
= (1+ sin(theta/2)/cos(theta/2)) / (1- sin(theta/2)/cos(theta/2)
= (cos(theta/2)+sin(theta/2)) / (cos(theta/2)-sin(theta/2))
= cos^2(theta/2)-sin^2(theta/2)
...._____________________________________________
....cos^2(theta/2) + sin^2(theta/2) - 2cos(theta/2)sin(theta/2)

= cos(theta) / (1 - sin(theta))



x+ (1/x) = 2cos(theta)
1/2(x + 1/x) = cos(theta)

2cos(2theta)
=2(2cos^2 theta - 1)
=2(2(1/2(x+1/x))^2 -1)
=2(2(1/4 (x^2 + 1/x^2 + 2))-1)
=2(1/2x^2 + 1/(2x^2) +1 -1)
=x^2 + (1/x^2)

Answer 2

I do not personally know the answer, but maybe this will help:
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