Question

If cosx = -3/5 and π/2 < x < π, find the value of

(i) sinx/2

(ii) cosx/2

(iii) tanx/2

Answer 1

Given: cosx = \(-\frac{3}{5}\) and \(\frac{\pi}{2}\) < x < π.ie, x lies in || quadrant

To Find:

(i) sin\(\frac{x}{2}\)

Formula used:

Since sinx is positive in || quadrant, hence sin\(\frac{x}{2}=\frac{2}{\sqrt{5}}\)

(ii) cos\(\frac{x}{2}\)

Formula used:

since cosx is negative in || quadrant, hence cos\(\frac{x}{2}\) = \(-\frac{1}{\sqrt{5}}\)

(iii) tan\(\frac{x}{2}\)

Formula used:

Here, tanx is negative in || quadrant.