Question

if sinA + cosA=✓2sin(90°-A) then prove that cotA=√2+1

Answer 1

Given Sin A + cos A = root 2 sin(90 - A)

           Sin A + cos A = root 2 cos A

          Squaring on both sides, we get

           (Sin A + cos A)^2 = (root 2 cos A)^2

           sin^2 A + cos ^2 A  + 2 sin A cos A = 2 cos^2 A

          1 + 2 Sin A cos A = 2 cos^2 A

          2 Sin A cos A = 2 cos ^2 A - 1

          Sin 2A = cos 2 A

          Tan 2 A = 1

          2A = 45

          A = 22.5.

   Multiply with cot on both sides, we get

       Cot A = cot 22.5

      Cot A = root 2 + 1.


Hop this helps! :)