In right triangle ABC, with right angle at C, AC=5 and BC=12. Find the value of (sin A)^2+ (sin B)^2

Step-by-step explanation:

Look at the picture.

We need the hypotenuse. Use the Pythagorean theorem:

Substitute

For angle A we have

Substitute:

For angle B we ahve

Substitute:

Substitute to given expression:

You can also see a relationship:

Therefore

It's a Pythagorean identity:

Therefore

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step-by-step explanation: