Question

If A and B are angles of a right angled triangle ABC right angled triangle at C prove that sin2 A + sin2 B = 1

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Answer 1

SOLUTION:-

Triangle ABC is right angled at C.

So,

According to the question;

C= 90°

A+B + C= 180° [property of ∆]

A+ B+ 90°= 180°

A+B= 180° -90°

A+B = 90°

B= 90° - A

So,

sin² A + sin²B

=) sin²A + sin² (90- A)

=)sin²A +cos² A

[because sin(90°-A)=cosA]

=) sin²A + cos²A = 1

Proved.

Hope it helps ☺️