Question

If cosx = tany, coty = tanz and cotz = tanx, then sinx =

please answer it fast

Best one as brainliest​

Answer 1

hope you will understand!

Answer 2

Answer:

Sinx = [-1+√5]/2 or [-1-√5]/2

Step-by-step explanation:

cosx = tany ........Eq(1)

tanz = coty .........Eq(2)

cotz = tanx .........Eq(3)

multiply Eq(1) Eq(2) and Eq(3)

cosx * tanz * cotz = tany * coty * tanx

here tanz and cotz get cancelled and tany and coty get cancelled,tan is the reciprocal of cot.

cosx = tanx

cosx = sinx/cosx

cos^2x = sinx

1-sin^2x = sinx

sin^2x + sinx - 1 = 0

it is a quadratic equation in variable sinx

sinx = [- 1 ± √(1²-4*1*-1)]2*1

         = [-1±√(1+4)]/2

         = [-1±√5]/2

therefore sinx = [-1+√5]/2 or [-1-√5]/2