...Prove that . + cos A 003-5- = !, ' 2 Which sign of the root is to bo taken if A > 180° < 270'? 7. In any triangle the sides are proportional to the sines of the opposite angles. Prove that cos A cos В _ l fsin B sin A\ ab ~ с (sin A sin B) ' 8. Prove the formula...

...as в is indefinitely diminished. 6. Expand log, (1 + x) in a series of powers of x. Prove that 7. In any triangle the sides are proportional to the sines of the angles opposite to them. Through the angular point С of a triangle ABС is drawn any line CMN on which...

...tanC(tanB - tan A)2 + 8 = - ±^ - "- - n2 \ m 2m? 4n2 u = — — o" x — ^ + " + 8 = -8 + 8 = 0. 84. In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, and let a perpendicular AD be 30 D AD = ABsinABC; also AD...

...=bcoaC + ecosB. [For, cos B = cos 90° = 0.] Similarly it may be proved that, 238. III. To prove that, in any triangle, the sides are proportional to the sines of the opposite angles ; or, To prove abc that sin A sin B sin 0 From A, any one of the angular points, draw...

...to construct an angle of 15°, and find from the construction the sine of 15°. (20.) 36. Show that in any triangle the sides are proportional to the sines of the opposita angles. AB is a lino 2,000 feet long; B is due east of A; at B a distant point P bears 46°...

...+ cos A sin B. Find what this formula becomes when B is replaced by ii's complement. 3. Prove that in any triangle the sides are proportional to the sines of the opposite angles. Prove that , J2 sin C + i3 sin B _ be sin A b + c ~ a 4. Shew how to solve a triangle,...

...In all cases the lengths of the sides opposite the angles A, B, C, are denoted by a, b, e. 128. I. In any triangle the sides are proportional to the sines of the opposite angles ; ie - — - = - — — = — — — . 1 l sт A sin В sin С Fig. 2. From one of...

...— — (г 7. tan2A = 2 ab V - a1' 8. sin3A = c2 S ab2 -a3 OBLIQUE TRIANGLES. 55. Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB. We have, then, in both figures...

...following : 1. tan B = cot A + cos C. 2. sin2A = sin2B. W -o? OBLIQUE TRIANGLES. 95. Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB. We have, then, in both figures...

...its sine is I, determine cos ^- by means of the expression (/3) of the last question. 5. Show that in any triangle the sides are proportional to the sines of the opposite angles. 6. If a straight line be drawn bisecting the angle A of a triangle ABC to meet the...