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

1 Answer
Feb 18, 2016

#f(theta)= 1/sqrt ( 1/2 +sqrt((1+cos theta)/8# + # sqrt ( 1/2 +sqrt((1+cos theta)/8#

Explanation:

=#sec theta/4 + sin(pi/2-theta/4)= 1/cos (theta/4 )+ cos (theta/4)#

#cos (theta/4)= sqrt(cos^2(theta/4))=sqrt(1/2 (1+cos(theta/2)#

=#sqrt(1/2 (1+sqrt (cos^2( theta/2)#

=#sqrt (1/2 (1+sqrt( 1/2 (1+cos theta)) #

=# sqrt ( 1/2 +sqrt((1+cos theta)/8#

Hence #f(theta)= 1/sqrt ( 1/2 +sqrt((1+cos theta)/8# + # sqrt ( 1/2 +sqrt((1+cos theta)/8#