Prove sin8-3cos23-6 - cos13-3sin35-6 - 12

LHS sin8π3cos23π6+cos13π3sin35π6 =sin (3π π3)cos (4π π6)+cos (4π+π3)sin (6π π6) =sinπ3cosπ6 cosπ3sinπ6 =sin (π3 π6) =sinπ6 =1 ...

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

Composition of Inverse Trigonometric Functions and Trigonometric Functions

Prove sin8π...

Question

Prove $sin \frac{8 π}{3} cos \frac{23 π}{6} + cos \frac{13 π}{3} sin \frac{35 π}{6} = \frac{1}{2}$

Open in App

Solution

Suggest Corrections

Similar questions

sin \frac{8 π}{3} cos \frac{23 π}{6} + cos \frac{13 π}{3} sin \frac{35 π}{6} = \frac{1}{2}

Prove that:

$(i) t a n 225^{\circ} c o t 405^{\circ} + t a n 765^{\circ} c o t 675^{\circ} = 0$

$(i i) s i n \frac{8 π}{3} c o s \frac{23 π}{6} + c o s \frac{13 π}{3} s i n \frac{35 π}{6} = \frac{1}{2}$

$(i i i) c o s 24^{\circ} + c o s 55^{\circ} + c o s 125^{\circ} + c o s 204^{\circ} + c o s 300^{\circ} = \frac{1}{2}$

$(i v) t a n (- 225^{\circ}) c o t (- 405^{\circ}) - t a n (- 765^{\circ}) c o t (675^{\circ}) = 0$

$(v) c o s 570^{\circ} s i n 510^{\circ} + s i n (- 330^{\circ}) c o s (- 390^{\circ}) = 0$

$(v i) t a n \frac{11 π}{3} - 2 s i n \frac{4 π}{6} - \frac{3}{4} c o s e c^{2} \frac{π}{4} + 4 c o s^{2} \frac{17 π}{6} = \frac{3 - 4 \sqrt{3}}{2}$

$(v i i) 3 s i n \frac{π}{6} s e c \frac{π}{3} - 4 s i n \frac{5 π}{5} c o t \frac{π}{4} = 1$

1^{2} + 2^{2} + 3^{2} + . . . . . . . x^{2} = \frac{x (x + 1) (2 x + 1)}{6}

1^{2} + 2^{2} + 3^{2} + . . . . + n^{2} = \frac{n (n + 1) (2 n + 1)}{6}

x = {log}_{12} 6, y = {log}_{18} 12

z = {log}_{24} 18

1 + x y z = 2 y z

Join BYJU'S Learning Program