Find the value of cot- 168-sin -1513 -

The correct options are A cos 11665 B sin 16365 C sin 1126130cot 168 nbsp;+ nbsp;sin 1513 =sin 1810 nbsp;+ nbsp;sin 1513 = nbsp;sin 1810×1 5132 nbsp ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Basic Inverse Trigonometric Functions

Find the valu...

Question

Find the value of
$c o t^{- 1} \frac{6}{8} + {sin}^{- 1} \frac{5}{13} .$

{cos}^{- 1} \frac{16}{65}

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

{sin}^{- 1} \frac{63}{65}

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

{sin}^{- 1} \frac{126}{130}

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

None

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

Open in App

Solution

The correct options are
A ${cos}^{- 1} \frac{16}{65}$
B ${sin}^{- 1} \frac{63}{65}$
C ${sin}^{- 1} \frac{126}{130}$
$c o t^{- 1} \frac{6}{8} + {sin}^{- 1} \frac{5}{13}$
$= {sin}^{- 1} \frac{8}{10} + {sin}^{- 1} \frac{5}{13}$
$= {sin}^{- 1} (\frac{8}{10} \times \sqrt{1 - {(\frac{5}{13})}^{2}} + \frac{5}{13} \times \sqrt{1 - {(\frac{8}{10})}^{2}}) = {sin}^{- 1} (\frac{8}{10} \times \frac{12}{13} + \frac{5}{13} \times \frac{6}{10}) = {sin}^{- 1} (\frac{96}{130} + \frac{30}{130}) = {sin}^{- 1} (\frac{126}{130}) = {sin}^{- 1} (\frac{63}{65}) = {cos}^{- 1} (\frac{16}{65})$

Suggest Corrections

Similar questions

Q. Prove the following results

(i)

\tan (\cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{2}{3}) = \frac{17}{6}

(ii)

\cos (\sin^{- 1} \frac{3}{5} + \cot^{- 1} \frac{3}{2}) = \frac{6}{5 \sqrt{13}}

(iii)

\tan (\sin^{- 1} \frac{5}{13} + \cos^{- 1} \frac{3}{5}) = \frac{63}{16}

(iv)

\sin (\cos^{- 1} \frac{3}{5} + \sin^{- 1} \frac{5}{13}) = \frac{63}{65}

Q. Find the value of

{cos}^{- 1} \frac{3}{5} + {cos}^{- 1} \frac{5}{13} .

Q. Find the value of

{cos}^{- 1} \frac{3}{5} + {cos}^{- 1} \frac{5}{13} .

Q. (i)

\sin^{- 1} \frac{63}{65} = \sin^{- 1} \frac{5}{13} + \cos^{- 1} \frac{3}{5}

(ii)

\sin^{- 1} \frac{5}{13} + \cos^{- 1} \frac{3}{5} = \tan^{- 1} \frac{63}{16}

(iii)

\frac{9 π}{8} - \frac{9}{4} \sin^{- 1} \frac{1}{3} = \frac{9}{4} \sin^{- 1} \frac{2 \sqrt{2}}{3}

Q. Find the value of x:

cot 4 x (sin 5 x + sin 3 x) = cot x (sin 5 x - sin 3 x)

Join BYJU'S Learning Program

Find the value of cot−168 + sin−1513.

The correct options are A cos−11665 B sin−16365 C sin−1126130cot−168 + sin−1513 =sin−1810 + sin−1513 = sin−1(810×√1−(513)2 + 513×√1−(810)2)= sin−1(810×1213 + 513×610)= sin−1 (96130 + 30130)= sin−1(126130)= sin−1(6365)= cos−1(1665)

Find the value of
$c o t^{- 1} \frac{6}{8} + {sin}^{- 1} \frac{5}{13} .$