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)))#