The sum of solutions of equation 2 sin -1-x2-x-1-cos -1-x2-x-3 -2 is - then - equals

0≤(x^2+x+1)≤ 1 and 0≤ (x^2+x)≤ 1 which holds together for x= 1, 0 At x= 1, L.H.S. = 2sin^ 1+cos^ 1 0 = π + π/2=3π/2 At x=0, L.H.S. = π+π/2=3π/2 Sum of the ...

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Standard XII

Mathematics

General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

The sum of so...

Question

The sum of solutions of equation $2 {sin}^{- 1} \sqrt{x^{2} + x + 1} + {cos}^{- 1} \sqrt{x^{2} + x} = \frac{3 π}{2}$ is $- λ$ then $λ$ equals

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Solution

$0 \leq (x^{2} + x + 1) \leq 1$ and $0 \leq (x^{2} + x) \leq 1$

which holds together for $x = - 1, 0$

At $x = - 1,$ L.H.S. $= 2 {sin}^{- 1} + {cos}^{- 1} 0$

$= π + \frac{π}{2} = \frac{3 π}{2}$

At $x = 0,$ L.H.S. $= π + \frac{π}{2} = \frac{3 π}{2}$

Sum of the solutions $= - 1 + 0 = - 1 = - λ$
$\Rightarrow λ = 1$

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The sum of solutions of equation 2sin−1√x2+x+1+cos−1√x2+x=3π2 is −λ then λ equals

0≤(x2+x+1)≤1 and 0≤(x2+x)≤1 which holds together for x=−1, 0 At x=−1, L.H.S. =2sin−1+cos−10 =π+π2=3π2 At x=0, L.H.S. =π+π2=3π2 Sum of the solutions =−1+0=−1=−λ ⇒λ=1

The sum of solutions of equation $2 {sin}^{- 1} \sqrt{x^{2} + x + 1} + {cos}^{- 1} \sqrt{x^{2} + x} = \frac{3 π}{2}$ is $- λ$ then $λ$ equals