Question

please solve these if possible

Q1. If sinx +siny=3(cosy-cosx) then the value of sin3x/sin3y.
Q2. If sina ,cosa,and tan a are in g.p.then cos cubea+cos square a is equal to

Answer 1

Q1.

From the given relation, we can write, 3 cos x + sin x = 3 cos y - sin y

put r cos ƒ¿=3 and r sin ƒ¿ = 1 , then we get , r = ã 10, tanƒ¿= 1/3

so r cos ( x - ƒ¿) = r cos (x+ƒ¿)

x = - y or x = }(y+ƒ¿)

clearly x = - y satisfies the equation

therefore, x = - y

so 3x = -3y

sin 3x = sin (-3y) = - sin 3y

sin 3x / sin 3y = -1

Answer 2

ƒ¿= Greek letter Alpha

Answer 3

Q2)Because sina, cosa, tana - g.p.

cos^2(a)=sina*tana=sin^2(a)/cosa
cos^2(a)=(1-cos^2(a))/cosa

cos^3(a)=1-cos^2(a)