Question

X,y,z are in ap then sinx -sinz/cosz -cosx=

Answer 1

Answer:

-cot(y)

Step-by-step explanation:

If x,y,z are in AP,

y-x = z-y = r (common difference)

z-x = 2r

(x+z)/2 = y

sinx - sinz = 2cos((x+z)/2)sin((x-z)/2)

=> 2cos(y)sin(-r)

cosz - cosx = -2sin((x+z)/2)sin((x-z)/2)

=> -2sin(y)sin(-r)

(sinx - sinz)/(cosz - cosx)

= 2cos(y)sin(-r) ÷ -2sin(y)sin(-r)

= -cot(y)