Question #d44e3

1 Answer
Bdub
Aug 22, 2017

see below

Explanation:

#sin theta + cos theta =1#

Use Linear Combination to change the equation to the form
C cos (x-D). That is,
A cos x + B sin x = C cos(x-D) where #C=sqrt(A^2+B^2)# and
#D=cos^-1(A/C)#

Since A and B are both positive it means that we are working in Quadrant I. Therefore,

#A=1, B=1, C = sqrt 2, D=cos^-1(1/sqrt2)=45^@#

Hence,

#sqrt 2cos (theta-45^@)=1#--> Solve for theta

#cos (theta-45^@)=1/sqrt2#

#theta-45^@=cos^-1(1/sqrt2) #

#theta-45^@=+-45^@#

#theta=45^@+-45^@#

#color(red)(theta=90^@ or color(red)theta =0#

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