Question

Sin theta +cos theta =√2(sin 90-theta) then what is the value of cos theta

Answer 1

let A = theta

sin A + cos A =√2 sin( 90°- A)

{sin ( 90°- A)= cosA}

(sin A + cos A) ^2=2 cos A
{(a+b)^2= a^2 + b^2 + 2ab}

sin^2 A + cos ^2 A +2 sinA cosA =2 cosA

{sin^2 A + cos ^2 A =1 }

1+ 2 sinA cosA =2 cosA

1+2 sinA cosA /2= cosA

Answer 2

Using rationalization after rearrangement.....