If sinx + cosx = 15 then cot x is equal to ________.
sinx + cosx = 15
We need to find the value of cotx.
If we square both sides of the given equation, we get,
sin2x+cos2x+2sinx.cosx=125
sin 2x = 125−1=−2425
sin2x can be written in terms of tanx.
2tanx1+tan2x=−2425
⇒ 12tan^x +25tanx + 12= 0
⇒ (3tanx+4)(4tanx+3)=0
⇒ tanx=−43 or−34