If the equation sin -1 x 2- x -1-cos -1 ax -1-2 has exactly two solutions- then a cannot have the integral value-sA- -1B- 0C- 1D- 2

The correct options are A 1 C 1 D 2 The given equation holds if x^2+x+1=ax+1 and 1≤ x^2+x+1≤1 ⇒ x (x+1+a) = 0 and 1 ≤ x ≤ 0 ⇒ x = 0 or a 1 and 1 ≤ x ...

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Byju's Answer

Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

If the equati...

Question

If the equation $s i n^{- 1} (x^{2} + x + 1) + c o s^{- 1} (a x + 1) = \frac{π}{2}$ has exactly two solutions, then a cannot have the integral value/s

-1

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Solution

The correct options are
A
-1

C
1

D
2

The given equation holds if $x^{2} + x + 1 = a x + 1 a n d - 1 \leq x^{2} + x + 1 \leq 1$

$\Rightarrow x (x + 1 + a) = 0$ and $- 1 \leq x \leq 0$

$\Rightarrow x = 0 o r a - 1 a n d - 1 \leq x \leq 0$

$∴ x = 0$ is one solution and for another different solution $- 1 \leq a - 1 < 0$

$\Rightarrow 0 \leq a < 1.$

So only integral value a can have is 0

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If the equation sin−1(x2+x+1)+cos−1(ax+1)=π2 has exactly two solutions, then a cannot have the integral value/s

The correct options are A -1 C 1 D 2 The given equation holds if x2+x+1=ax+1 and −1≤x2+x+1≤1 ⇒x(x+1+a)=0 and −1≤x≤0 ⇒x=0 or a−1 and −1≤x≤0 ∴x=0 is one solution and for another different solution −1≤a−1<0 ⇒0≤a<1. So only integral value a can have is 0

If the equation $s i n^{- 1} (x^{2} + x + 1) + c o s^{- 1} (a x + 1) = \frac{π}{2}$ has exactly two solutions, then a cannot have the integral value/s