First slide

Trigonometric transformations

Question

If sin( y+z -x), sin(z + x-y), sin(x + y - z) are in A.P, then tanx, tany, tanz are in

Moderate

A

A.P
B

G.P.
C

H.P
D

none of these

Solution

Applying b - a= c - b for A.P.,
we get 2 cosz sin(x - y) - 2 cosx sin(y - z)
Dividing by 2 cosx cosy cosz, etc.,
we get tanx-tany =tany -tanz

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