Prove that 2 sin- 6 - 3 - 4 sin 5 - 6 - 4 - 0

2sin(π/6)>sec(π/3) 4sin(5π/6)>cot(π/4) =2×(1/2)× #10;2 4sin(π (π/6))× 1 =2 4sin(π/6) =2 4×(1/2) =2 2=0 ...

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General Solution of Trigonometric Equation

Prove that ...

Question

Prove that
$2 sin \frac{π}{6} sec \frac{π}{3} - 4 sin \frac{5 π}{6} cot \frac{π}{4} = 0$

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3 sin \frac{π}{6} sec \frac{π}{3} - 4 sin \frac{5 π}{6} cot \frac{π}{4} = 1

Prove that:

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

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

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

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

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

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

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

\int_{0}^{1} \frac{c o s x}{1 + x} d x = K a n d \int_{6 π - 3}^{6 π} \frac{c o s (\frac{x}{3})}{6 π + 3 - x} d x = m K

\int_{π / 6}^{π / 4} cos 2 x d x =

\int_{\frac{π}{6}}^{\frac{π}{4}} c o s e c 2 x d x =

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