Solve: #1/sqrt(2)(sin Theta + cos Theta) = cos Theta# for #Theta in (0, pi/2)# ?

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Answer 1 · 2016-01-14T02:56:54

#Theta = pi/8# rad # = 22.5^o # for #Theta in (0, pi/2)#

#sin(A+B)=sin A cos B + cos A sin B#

Thus: #sin(Theta + pi/4)# = #sin Theta . cos (pi/4) + cos Theta . sin (pi/4)#

#= sin Theta . 1/sqrt(2) + cos Theta . 1/sqrt(2)#

Therefore from the equation in the question:

#sin Theta . 1/sqrt(2) + cos Theta . 1/sqrt(2) = cos Theta#

Divide through by #cos Theta#

#tan Theta . 1/sqrt(2) + 1/sqrt(2) = 1#

#tan Theta + 1 = sqrt(2)#

#tan Theta = sqrt(2) - 1#

#Theta = arctan(sqrt(2) - 1)#

#Theta = pi/8# rad # = 22.5^o# for #Theta in (0, pi/2)#