Question

1. Find tan x/2 if sin x = 4/5
(2).​

Answer 1

We know that

tan(x)=sin(x)cos(x)

And

cos(x)=1−sin2(x)−−−−−−−−−√

Because sin2(x)+cos2(x)=1 .

So, we have

tan(x)=sin(x)cos(x)=sin(x)⋅1cos(x)

=45⋅1cos(x)

We need to find cos(x) :

cos(x)=1−(45)2−−−−−−−−√

cos(x)=1−1625−−−−−−√

We know that 1=2525 . So, we have

cos(x)=925−−−√=9–√25−−√

cos(x)=35

So,

1cos(x)=135=53

Put this result in tan(x)=sin(x)⋅1cos(x) :

tan(x)=45⋅53

tan(x)=43

tan(x)=1.3333333333...

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