If sin-1 a + sin-1b + sin-1c = π , then find the value of a√1-a2+b√1-b2+c√1-c2.

Question

If sin-1 a + sin-1b + sin-1c = π , then find the value of a√1-a2+b√1-b2+c√1-c2. (A) abc (B) a + b + c (C) (1/a)×(1/b)×(1/c) (D) 2abc

Tardigrade Admin · Accepted Answer

Let sin-1 a = x ∴ a = sin x sin-1 b = y ∴ b = sin y sin-1 c = z ∴ c = sin z ∴ a√1-a2+b√1-b2+c√1-c2 = sin x cos x + sin y cosy + sinz cosz=(1/2) (sin2x + sin2y + sin 2z) = (1/2) (4sin x sin y sin z) = 2 sinx siny sinz = 2abc

Q. If $s i n^{- 1} a + s i n^{- 1} b + s i n^{- 1} c = π$ , then find the value of $a 1 - a^{2} + b 1 - b^{2} + c 1 - c^{2} .$

$ab c$

$a + b + c$

$\frac{1}{a} \times \frac{1}{b} \times \frac{1}{c}$

$2 ab c$

Q. If sin−1a+sin−1b+sin−1c=π, then find the value of a1−a2​+b1−b2​+c1−c2​.

abc

a+b+c

a1​×b1​×c1​

2abc

Let sin−1a=x∴a=sinx sin−1b=y∴b=siny sin−1c=z∴c=sinz ∴a1−a2​+b1−b2​+c1−c2​ =sinxcosx+sin<br/>ycosy+sinzcosz=(1/2)(sin2x+sin2y+sin2z)=(1/2)(4sinxsinysinz) =2sinxsinysinz =2abc

Q. If $s i n^{- 1} a + s i n^{- 1} b + s i n^{- 1} c = π$ , then find the value of $a 1 - a^{2} + b 1 - b^{2} + c 1 - c^{2} .$

$ab c$

$a + b + c$

$\frac{1}{a} \times \frac{1}{b} \times \frac{1}{c}$

$2 ab c$