Question

if A and B are angle of right angled triangle ABC right angled at C prove that sin ^2A +sin^2B =1.​

Answer 1

Answer:

We can consider triangle ABC as a right triangle. But most appropriately we can say it a right isosceles triangle.

As its terms also satisfy the law:

sin2A+sin2B+sin2C=2+2cosA.cosB.cosC

Thus, 2cosA.cosB.cosC can only be diminished if one of them is right angle.

Answer 2

Step-by-step explanation:

Consider a triangle ABC(as given, 90° at C).

Since, A + B + C = 180° & C is 90°.

=> A + B + 90° = 180°

=> A = 90° - B

As we know, in any triangle, sin²x + cos²x = 1 & cos(90 - ∅) = sin∅.

So, cosA = cos(90° - B) {A= 90°-B}

cosA = sinB {cos(90 - ∅) = sin∅}

Using sin²x + cos²x = 1,

=> sin²A + cos²A = 1

=> sin²A + sin²B = 1 {cosA = sinB}

As desired, sin²A + sin²B = 1