If sin -11-3-sin -12-3-sin -1 x- then x is equal toA- NB- -5-4 -2-9C- -5-4 -2-9D- x-2

The correct option is C √(5)+4√(2)/9sin^ 11/3 + sin^ 12/3 = sin^ 1 [ 1/3√(1 4/9) + 2/3√(1 1/9) ] = sin^ 1 [ √(5) + 4√(2)/9 ] Therefore x = √(5)+4√(2)/9 ...

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

Byju's Answer

Standard XII

Mathematics

Properties Derived from Trigonometric Identities

If sin -11/3+...

Question

If ${sin}^{- 1} \frac{1}{3} + {sin}^{- 1} \frac{2}{3} = {sin}^{- 1} x,$ then $x$ is equal to

0.0

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

\frac{\sqrt{5} - 4 \sqrt{2}}{9}

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

\frac{\sqrt{5} + 4 \sqrt{2}}{9}

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

\frac{x}{2}

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

Open in App

Solution

The correct option is C $\frac{\sqrt{5} + 4 \sqrt{2}}{9}$
${sin}^{- 1} \frac{1}{3} + {sin}^{- 1} \frac{2}{3} = {sin}^{- 1} [\frac{1}{3} \sqrt{1 - \frac{4}{9}} + \frac{2}{3} \sqrt{1 - \frac{1}{9}}] = {sin}^{- 1} [\frac{\sqrt{5} + 4 \sqrt{2}}{9}]$
Therefore $x = \frac{\sqrt{5} + 4 \sqrt{2}}{9}$

Suggest Corrections

Similar questions

Q. If

{sin}^{- 1} x + {cot}^{- 1} (\frac{1}{2}) = \frac{π}{2},

then

x

is equal to

Q. If

s i n^{- 1} (\frac{1}{3}) + s i n^{- 1} (\frac{2}{3}) = s i n^{- 1} x

, then x is equal to

\frac{s i n 7 x + 6 s i n 5 x + 17 s i n 3 x + 12 s i n x}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x}

is equal to

Q. If

\int \frac{c o s^{7} x + c o s^{5} x}{s i n^{2} x + s i n^{4} x} d x = - \frac{A}{744} s i n^{3} x + 5 s i n x - \frac{2}{s i n x} - 12 t a n^{- 1} (s i n x) + C

then A is equal to

Q. If

cos x

+ {cos}^{2} x = 1

then

{sin}^{12} x + 3 {sin}^{10} x +

3 {sin}^{8} x + {sin}^{6} x + {sin}^{4} x + 2 {sin}^{2} x - 2

is equal to

Join BYJU'S Learning Program

If sin−113+sin−123=sin−1x, then x is equal to

The correct option is C √5+4√29sin−113+sin−123=sin−1[13√1−49+23√1−19]=sin−1[√5+4√29] Therefore x=√5+4√29

If ${sin}^{- 1} \frac{1}{3} + {sin}^{- 1} \frac{2}{3} = {sin}^{- 1} x,$ then $x$ is equal to

The correct option is C $\frac{\sqrt{5} + 4 \sqrt{2}}{9}$
${sin}^{- 1} \frac{1}{3} + {sin}^{- 1} \frac{2}{3} = {sin}^{- 1} [\frac{1}{3} \sqrt{1 - \frac{4}{9}} + \frac{2}{3} \sqrt{1 - \frac{1}{9}}] = {sin}^{- 1} [\frac{\sqrt{5} + 4 \sqrt{2}}{9}]$
Therefore $x = \frac{\sqrt{5} + 4 \sqrt{2}}{9}$