How do you simplify $f(theta)=sec(theta/4)+2cos(theta/4-pi/2)$ to trigonometric functions of a unit $theta$ ?

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Answer 1 · 2016-07-07T09:16:37

$f(theta)=sec(theta/4)+2cos(theta/4-pi/2)$

$=sec(theta/4)+2cos(pi/2-theta/4)$

$=1/cos(theta/4)+2sin(theta/4)$

$=(1+2sin(theta/4)cos(theta/4))/cos(theta/4)$

$=(1+sin2theta/4)/(cos(theta/4))$

$=(1+sin(theta/2))/sqrt(1/2(1+cos(theta/2)))$

$=(1+sqrt(1/2(1-costheta)))/sqrt(1/2(1+sqrt(1/2(1+costheta)))$

How do you simplify f(theta)=sec(theta/4)+2cos(theta/4-pi/2)f(theta)=sec(theta/4)+2cos(theta/4-pi/2) to trigonometric functions of a unit thetatheta?