Question

Question #d44e3

Answer 1

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`