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in Trigonometry by (15 points)
The value of cos.tan^-1, cot.cos^-1 root 3/2 is

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Let θ = tan-1\(\frac{\sqrt3}{2}\)

tanθ = \(\frac{\sqrt3}{2}\) \(\Rightarrow\) L = \(\sqrt3\), A = 2 , K = \(\sqrt{4+3}\) = \(\sqrt7\)

cosθ = \(\frac{2}{\sqrt7}\) \(\Rightarrow\) θ = cos-1\(\big(\frac{2}{\sqrt7}\big)\)

cos\(\big(\tan^{-1}\frac{\sqrt3}{2}\big)\) = cos\(\big(\cos^{-1}\frac{\sqrt2}{7}\big)\) = \(\frac{2}{\sqrt7}\)

cot\(\big(\cos^{-1}\frac{\sqrt3}{2}\big)\) = cot\(\big(\frac{\pi}{6}\big)\) = \(\sqrt3\)  \(\Big(\)\(\because\) cos\(\frac{\pi}{6}\) = \(\frac{\sqrt3}{2}\), cot \(\frac{\pi}{6}\) = \(\sqrt3\)\(\Big)\)

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