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