Question

in right angle triangle , sin^2A + sin^2B + sin^2C is-----------------. a) 2 b1 c)-1 d)0​

Answer 1

Answer:

Let us say that the triangle ABC has the angle C as 90° .

Considering A and B to be acute angles ( less than 90° ) we know by trigonometric relations that :

sin²A + cos²A = 1

Now in Δ ABC , we have :

∠A + ∠B + ∠C = 180

We know that ∠C = 90° .

Hence :

∠A + ∠B + 90° = 180°

⇒ ∠A + ∠B = 90°

⇒ ∠A = 90° - ∠B

sin²A + sin²B + sin²C

⇒ sin²A + sin²( 90 - A ) + sin² ( 90 )

By trigonometry we know sin 90 = 1 , also we know that sin² ( 90 - B ) = cos²A

⇒ sin²A + cos²A + 1²

⇒ 1 + 1

⇒ 2

Hence the value will be 2 .

OPTION A is correct .

Step-by-step explanation:

Angle sum property of a triangle states that the sum of all angles of a triangle is 180 degrees .

We use sin²A + cos²A = 1 when A is an acute angle .