The equation is 2 cos-1 x - sin-1 x - 11 -6 has-AMU 1999

Given equation is (2 cos^ 1 x + sin^ 1 x = 11 π/6 ⇒ cos^ 1 x + (cos^ 1 x + sin^ 1x) = 11 π/6 ⇒ cos^ 1 x + π/2 = 11 π/6 ⇒ cos^ 1 x + 4 π/3 which is not possible ...

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Standard XII

Mathematics

Properties Derived from Trigonometric Identities

The equation ...

Question

The equation is $2 c o s^{- 1} x + s i n^{- 1} x = \frac{11 π}{6}$ has
[AMU 1999}

No solution

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Solution

The correct option is A No solution
Given equation is $(2 c o s^{- 1} x + s i n^{- 1} x = \frac{11 π}{6}$
$\Rightarrow c o s^{- 1} x + (c o s^{- 1} x + s i n^{- 1} x) = \frac{11 π}{6} \Rightarrow c o s^{- 1} x + \frac{π}{2} = \frac{11 π}{6} \Rightarrow c o s^{- 1} x + 4 π / 3$
which is not possible as $c o s^{- 1} x ε [0, π]$

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The equation is 2 cos−1 x+sin−1 x=11π6 has [AMU 1999}

The correct option is A No solutionGiven equation is (2 cos−1 x+sin−1 x=11π6 ⇒cos−1 x+(cos−1 x+sin−1x)=11π6⇒cos−1 x+π2=11π6⇒cos−1 x+4π/3 which is not possible as cos−1 x ε[0,π]

The equation is $2 c o s^{- 1} x + s i n^{- 1} x = \frac{11 π}{6}$ has
[AMU 1999}