Question

If sinA+cosA=√2cosA,show that,tan2A=1

Answer 1

I hope it helps you

Answer 2

Answer:

tan 2A = 1

Step-by-step explanation:

=> sin A + cos A = root2 cos A

=> sin A = root2 cos A - cos A

=> sin A = cos A (root2 - 1)

=> sin A / cos A = root2 - 1

=> tan A = root2 - 1

NOW,

=> tan 2A = 2 tan A / 1 - tan^2 A

=> tan 2A = 2 (root2 - 1) / 1 - (root2 - 1)^2

=> tan 2A = 2 (root2 - 1) / 2 root2 - 2

=> tan 2A = 2 (root2 - 1) / 2 (root2 - 1)

=> tan 2A = 1

[PROVED]

HOPE IT WILL HELP YOU