# Find if <im

Given that x is in quadrant II

So,

180° < x < 270°

Dividing with 2 all sides

(180°/2) < x/2 < (270°/2)

90° < x/2 < 135° lies in 2nd quadrant

sin is positive and cos, tan are negative is positive and are negative

Given

cos x = -(1/3)

We know that

cos 2x = 2 cos2x - 1

Replacing x with x/2

cos 2(x/2) = 2 cos2(x/2) - 1

cos x = 2 cos2(x/2) - 1

-1/3 = 2 cos2(x/2) - 1

2/3 = 2 cos2(x/2)

cos2(x/2) = 1/3

cos(x/2) = (1/√3) lies in 2nd quadrant is negative  Now,

We know that

1 + tan2x = sec2x

Replacing x with x/2      lies in 2nd quadrant is positive in 2nd quadrant We know that- Replacing x with x/2  Hence, Rate this question :

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