is true when n=1, prove that it will be true when n is any positive integer. 5. If a cos 0+b sin 0=c and a cos2+b sin2 (=c, prove that 4a2b2+(b−c) (a — c) (a — b)2=0. 6. Prove the following identities: (i) (ii) (iii) sin (B-y) cos (a — B) cos (a− y) = − II sin (ẞ − y); sin a sin (B-y) cos (B+y− a)=0; sin a sin (ß− y) sin (B+y− a)=2II sin (ẞ − y). 7. If P be a point within a triangle ABC, such that prove that (1) (2) LPAB=LPBC= LPCA=w, cot w=cot A+cot B+cot C; cosec2 w=cosec2 A+cosec2 B+cosec2 C. 8. A hill of inclination 1 in 169 faces West. Shew that a railway on it which runs S.E. has an inclination of 1 in 239. 9. Two vertical walls of equal height a are inclined to one another at an angle a. At noon the breadth of their shadows are b and c shew that the altitude of the sun is given by the equation a2 sin2 y cot2 = b2+c2+2bc cos y. |