The equation is 2 cos -1 x -sin -1 x -11 -6 has-AMU 1999A- No solutionB- Two solutionsC- Only one solutionD- Three solutions

The correct option is A No solutionGiven 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 ...

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

Byju's Answer

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Only one solution

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Two solutions

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Three solutions

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $c o s^{- 1} x ε [0, π]$

Suggest Corrections

Similar questions

Q. The equation

2 {cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}

has

Q. Solve

2 {cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}

3 c o s^{- 1} x - π x - \frac{π}{2} = 0

has :

The pair of equations y = 0 and y = -7 has :

Q. Mark (✓) against the correct answer in each of the following:
The equation 2x + 3y = 6 has
(a) a unique solution
(b) only two solutions
(c) no solution
(d) infinitely many solutions

Join BYJU'S Learning Program

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}