If `A=75^@,B=45^@,` then prove that `b+csqrt(2)=2a`

If A+B=45^(@) then prove that (1+tan A)(1+tan B)=2. On the basis of the result obtained prove that tan22.5^(0)=sqrt(2)-1

If A=2B, then prove that either c=b or a^(2)=b(c+b)

If x+y=45^(@) , then prove that: a) (1+tanx)(1+tany)=2 b) (cotx-1)(coty-1)=2

In a DeltaABC , if A=45^(@) and B=75^(@) , then a+sqrt(2)c=

Prove that: (a-b)^(2)=a^(2)-2ab+b^(2)

If cot A=(b)/(a) ,then prove that : (asin - b cosA)/(sin A+bcosA)=(a^(2)-b^(2))/(a^(2)+b^(2))