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Answer:
Before solving this problem, we will need to know a few formulas such as:
1-cosx= 2sin²(x/2)………………………………………(1)
And,
sin x=2sin(x / 2).cos(x / 2)…………………………(2)
Hence, from (1) and (2), we get
(1-cos x)/sin x = {2sin²(x/2)}/2sin(x/2).cos(x/2)
On taking 2sin(x/2) common and cancelling, we get
(1-cos x)/sin x= sin (x/2)/cos(x/2)
Therefore,
As sin x/cos x = tan x
Thus,
(1-cos x)/sin x=tan(x / 2)
Hence, it can be concluded that the value of (1-cos x)/sin x is equal to tan (x/2).
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