If -i-110sin-1xi-5- then the value of -i-110xi2 is

Given : ∑_i=1^10sin^ 1x_i=5π ⇒sin^ 1x_1+sin^ 1x_2+⋯+sin^ 1x_10=5π We know that, sin^ 1x∈[ π2,π2] ∴ The above equation is valid only when sin^ 1x_i=π2⇒ x_i=1 ∴∑_ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Property 6

If ∑i=110sin-...

Question

If $10 \sum i = 1 {sin}^{- 1} x_{i} = 5 π$ , then the value of $10 \sum i = 1 x_{i}^{2}$ is

Open in App

Solution

Given : $10 \sum i = 1 {sin}^{- 1} x_{i} = 5 π$
$\Rightarrow {sin}^{- 1} x_{1} + {sin}^{- 1} x_{2} + \dots + {sin}^{- 1} x_{10} = 5 π$
We know that, ${sin}^{- 1} x \in [- \frac{π}{2}, \frac{π}{2}]$
$∴$ The above equation is valid only when ${sin}^{- 1} x_{i} = \frac{π}{2} \Rightarrow x_{i} = 1 ∴ 10 \sum i = 1 x_{i}^{2} = 10$

Suggest Corrections

Similar questions

Q. If the function

f (x) = \frac{2 x - \sin^{- 1} x}{2 x + \tan^{- 1} x}

is continuous at each point of its domain, then the value of f (0) is
(a) 2

(b)

\frac{1}{3}

(c)

- \frac{1}{3}

(d)

\frac{2}{3}

Q. If

\sum_{i = 1}^{10} x_{1} = 60

and

\sum_{i = 1}^{10} x_{i}^{2} = 360

then

\sum_{i = 1}^{10} x_{i}^{3}

Q. If M =

\frac{x_{1} + x_{2} + . . . + x_{20}}{20}

, then the value of

\sum_{i - 1}^{20} \frac{(x_{i} - M)}{20}

Q. If

M = \frac{x_{1} + x_{2} +_{20}}{20}

then the value of

20 \sum i = 1 \frac{(x_{i} - M)}{20}

Q. If

2 n \sum i - 1 {sin}^{- 1} x_{i} = n π

, then show that

2 n \sum i = 1 x_{i} = 2 n

Join BYJU'S Learning Program

Explore more

Property 6

Standard XII Mathematics

Join BYJU'S Learning Program

If 10∑i=1sin−1xi=5π, then the value of 10∑i=1x2i is

Given : 10∑i=1sin−1xi=5π ⇒sin−1x1+sin−1x2+⋯+sin−1x10=5π We know that, sin−1x∈[−π2,π2] ∴ The above equation is valid only when sin−1xi=π2⇒xi=1∴10∑i=1x2i=10

If $10 \sum i = 1 {sin}^{- 1} x_{i} = 5 π$ , then the value of $10 \sum i = 1 x_{i}^{2}$ is