If sin-1 sin 33 -7 -cos-1 cos 46 -7 -tan-1 -tan 13 -8 -cot-1 cot -19 -8 -a -b Where a and b are in their lowest form- then a - b equal to

On solving, we get aπ/b=13 π/7⇒ 13+7=20. ...

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Composition of Inverse Trigonometric Functions and Trigonometric Functions

If sin-1 sin ...

Question

If $s i n^{- 1} (s i n \frac{33 π}{7}) + c o s^{- 1} (c o s \frac{46 π}{7}) + t a n^{- 1} (- t a n \frac{13 π}{8}) + c o t^{- 1} (c o t (- \frac{19 π}{8})) = \frac{a π}{b}$ Where a and b are in their lowest form, then (a + b) equal to

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y = {sin}^{- 1} (sin 8) - {tan}^{- 1} (tan 10) + {cos}^{- 1} (cos 12) - {sec}^{- 1} (sec 9) + {cot}^{- 1} (cot 6) - {cosec}^{- 1} (cosec 7) .

y

a π + b,

a - b

\frac{\sin A + \sin B}{\sin A - \sin B} = \tan (\frac{A + B}{2}) \cot (\frac{A - B}{2})

\frac{\sin A + \sin 3 A}{\cos A - \cos 3 A} = \cot A

\frac{\sin 9 A - \sin 7 A}{\cos 7 A - \cos 9 A} = \cot 8 A

\frac{\cos A + \cos B}{\cos B - \cos A} = \cot (\frac{A + B}{2}) \cot (\frac{A - B}{2})

\frac{\sin A - \sin B}{\cos A + \cos B} = \tan \frac{A - B}{2}

A = sin \frac{2 π}{7} + sin \frac{4 π}{7} + sin \frac{8 π}{7}

B = cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{8 π}{7}

\sqrt{A^{2} + B^{2}}

A = sin \frac{2 π}{7} + sin \frac{4 π}{7} + sin \frac{8 π}{7}

B = cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{8 π}{7}

A^{2} + B^{2}

A = sin \frac{2 π}{7} - sin \frac{4 π}{7} + sin \frac{8 π}{7}

B = cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{8 π}{7}

\sqrt{A^{2} + B^{2}}

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