First slide

Trigonometric transformations

Question

If $\sin (y + z - x), \sin (z + x - y), \sin (x + y - z)$ are in A.P., then tan x, tan y, tan z 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
$2 \cos zsin (x - y) = 2 \cos xsin (y - z)$
Dividing by 2 cosx cosy cosz, etc., we get
tanx-tany = tany-tanz

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