Question

if sinA+cosA=root 2 cosA then find the value of cotA.pls answer fast as tomorrow is my maths exam

Answer 1

solution:

sin A + cos A =√cos A

then,  sin A=√cos A - cos A
           sin A=√cos A(1-√(cosA))......(i)

As we know,
           cot A = cos A / sin A
           cot A = cosA/√(cosA)(1-√(cosA))
          
              cot A =√(cos A)/(1-√(cos A)) 
              cot A =√(cos A)/(1-√(cos A)) x (1+√(cos A)/1+√(cos A))  (By taking conjugate)
              cot A =√(cosA)(1+√(cosA))/1-cosA
              cot A =[√(cosA) + cosA/1-cos A] x (cos A+ 1/cos A + 1) (again taking conjugate)
              cot A =[{√(cosA) + cosA}(cosA+1)}/1-cos^2A]
             
            ∴cot A =(cosA√(cosA)+√(cosA)+cos^2A+cosA)/sin^2A

                Hope it Helps..!