If it is given that Sin A = Cos A then calculate Cos 2A?

Question

If
Sin A + Cos A = sqrt(2) Sin (90 - A)
then
Cot A = ??

Answer 1

Sin A=Cos A
implies A=45 degress
Cos 2A= Cos 2(45)=Cos 90=0

Answer 2

Ans : 0

Use the the formula.
cos (A+B) = cos A cos B - Sin A Sin B

So in our case :
cos 2A = Cos (A + A)
= cos A cos A - sin A sin A
since: cos A = sin A
so
= cos^2 A - cos^2 A
= 0

Answer 3

Sin A = Cos A

Divide by Cos A gives us Tan A = 1 i.e. A is 45

so Cos 2A is Cos 90 which is zero

Answer 4

Use the the formula.
cos (A+B) = cos A cos B - Sin A Sin B

So in our case :
cos 2A = Cos (A + A)
*Sin A = CosA **
implies A=45 degress
Cos 2A= Cos 2(45)=Cos 90=0
so the right answer is zero(0)