Given: cos\(\frac{x}{2}\) = \(\frac{12}{13}\) and x lies in Quadrant I i.e, All the trigonometric ratios are
positive in I quadrant
To Find:
(i) sin x
(ii) cos x
(iii) cot x
We have, sin x = \(\sqrt{1-cos^2\text{x}}\)
We know that, cos\(\frac{x}{2}\) = \(\sqrt{\frac{1+cosx}{2}}{}\)
(∵ cosx is positive in | quadrant)
Since, sinx = \(\sqrt{1-cos^2\text{x}}\)
Hence, we have sinx = \(\frac{120}{169}.\)
(ii) cosx
Formula used:
We know that, cos\(\frac{x}{2}\) = \(\sqrt{\frac{1+cosx}{2}}{}\)
(∵ cosx is positive in | quadrant)
(iii) cotx
Formula used:
Hence, we have cotx = \(\frac{119}{120}\)
