Question

If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.

Answer 1

We have , `(sin theta + cos theta ) = sqrt(2) cos theta`

Dividing both sides by sin θ , We get 

 `(sin theta)/ (sin theta )+ (cos theta)/ (sin theta)= (sqrt(2) cos theta)/ (sin theta)`

⇒ `1+ cot theta = sqrt(2) cot theta`

       ⇒ `sqrt(2) cot theta - cot theta =1` 

⇒ `( sqrt(2) - 1 ) cot theta =1`

`⇒ cot theta = 1/ (( sqrt(2)-1))`

`⇒ cot theta = 1/((sqrt(2)-1))xx ((sqrt(2)+1))/((sqrt(2)+1))`

`⇒ cot theta = ((sqrt(2)+1))/(2-1)`

`⇒ cot theta = ((sqrt(2)+1))/1`

∴`cot theta = (sqrt (2) +1)`