Prove that- 3sin-6-3-4sin5-6-4-1

LHS=3sinπ6π3 4sin5π6π4 =3(12)(2) 4sin(π π6).1 =3 4sinπ6=3 4(12)=3 2 =1 =RHS ...

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General Solution of Trigonometric Equation

Prove that: ...

Question

Prove that:
$3 sin \frac{π}{6} sec \frac{π}{3} - 4 sin \frac{5 π}{6} cot \frac{π}{4} = 1$

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

Prove that:

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

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

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

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

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

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

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

sin 0^{c} + 2 cos 0^{c} + 3 sin {(\frac{π}{2})}^{c} + 4 cos {(\frac{π}{2})}^{c} + 5 sec 0^{c} + 6 csc {(\frac{π}{2})}^{c} = ?

\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 / 3} \frac{d x}{1 + \sqrt{cot x}}

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