Sin ( 4tan^ 11/3 )=sin [ 2tan^ 1 ( 2/3/1 ( 1/9 ) ) ] sin ( 2tan^ 13/4 )=sin sin^ 1 ( 2× ( 3/4 )/1+ ( 9/16 ) ) =3/2×16/25=24/25 ( ∵ 2 tan^ 1x=sin^ 12x/1+x ...

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

Byju's Answer

Standard XIII

Mathematics

Properties Derived from Trigonometric Identities

sin 4tan-11/3...

Question

$s i n (4 t a n^{- 1} \frac{1}{3}) =$

\frac{12}{25}

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

\frac{24}{25}

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

\frac{1}{5}

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

None of these

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

Open in App

Solution

The correct option is B $\frac{24}{25}$
$s i n (4 t a n^{- 1} \frac{1}{3}) = s i n [2 t a n^{- 1} (\frac{\frac{2}{3}}{1 - (\frac{1}{9})})]$
$s i n (2 t a n^{- 1} \frac{3}{4}) = s i n s i n^{- 1} (\frac{2 \times (\frac{3}{4})}{1 + (\frac{9}{16})})$
$= \frac{3}{2} \times \frac{16}{25} = \frac{24}{25}$ $(∵ 2 t a n^{- 1} x = s i n^{- 1} \frac{2 x}{1 + x^{2}})$

Suggest Corrections

Similar questions

cos (2 tan^{- 1} \frac{1}{7}) - sin (4 tan^{- 1} \frac{1}{3}) =

Show that cos $(2 t a n^{- 1} \frac{1}{7}) = s i n (4 t a n^{- 1} \frac{1}{3}) .$

Q. The value of

sin (4 {tan}^{- 1} \frac{1}{3}) - cos (2 {tan}^{- 1} \frac{1}{7})

cos ({cos}^{- 1} \frac{1}{3} + {cos}^{- 1} \frac{1}{5}) + cos ({sin}^{- 1} \frac{1}{3} + {sin}^{- 1} \frac{1}{5}) =

__________

Q. Solve

(3 - \sqrt{11}) (3 + \sqrt{11})

Join BYJU'S Learning Program

sin(4tan−113)=

The correct option is B 2425 sin(4tan−113)=sin[2tan−1(231−(19))] sin(2tan−134)=sin sin−1(2×(34)1+(916)) =32×1625=2425 (∵2tan−1x=sin−12x1+x2)

$s i n (4 t a n^{- 1} \frac{1}{3}) =$