Question #d44e3

1 Answer
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