Question

If a and b are angles of right angled triangle abc right angled at c prove that sin2a + sin2b = 1

Answer 1

Sin2A+Sin2B.
B=90-A by angle sum property of a traingle
=Sin2A+Sin2A(90-A)
Sin90-A=CosA
=Sin2A+Cos2A
Now ,Sin2A+Cos2A=1. By identity

Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

Given if a and b are angles of right angled triangle abc right angled at c.

We have to prove that $sin^2a+sin^2b=1$

As, by angle sum property of triangle

a+b+c=180°

⇒ a+b+90=180°

⇒ b=180-90-a=90-a

$sin^2a+sin^2b=sin^2a+sin^2(90-a)$

                         $=sin^2a+(sin(90-a))^2$

                         $=sin^2a+cos^2a=1$

Hence Proved