Question

ABC is a right angled triangle at C prove that (1) tanAtanB=1 (2) sinAcosB+cosAsinB=1​

Answer 1

Answer:

Step-by-step explanation:

A+B+C = 180; ∠C = 90°

A+B = 180 - C = 180 - 90 = 90°.

1) Tan(A+B) = Tan90°

//But Tan(A+B) = TanA + TanB/ 1 - TanATanB

   TanA + TanB / 1 - TanATanB = 1/0   (∵Tan90 = Sin90/Cos90 = 1/0)

   1 - TanATanB = 0

   => TanATanB = 1.

Hence proved

2) Sin(A+B) = Sin90

//But Sin(A+B) = SinACosB + CosASinB

=> SinACosB + CosASinB = Sin90 = 1.

Hence proved