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Chapter 19: Problem 1848
If the roots of the quadratic equation \(4 x^{2}-4 x+1=\cos ^{2} \theta\) is \(a\) and \(\beta\) then \(\alpha+\beta=\) (a) \(\cos ^{2}(\theta / 2)\) (b) \(\sin ^{2}(\theta / 2)\) (c) 1 (d) \(2 \cos ^{2}(\theta / 2)\)
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If \(2 \tan \alpha+\cot \beta=\tan \beta\) then \(\tan (\beta-\alpha)=\) (a) tana (b) cota (c) \(\tan \beta\) (d) \(\cot \beta\)
If \(\cos x=\cos y=\cos z\) then \(\tan [(x+y) / 2] \tan [(x-y) / 2]=\) (a) \(\tan ^{2}(x / 2)\) (b) \(\tan ^{2}(\mathrm{y} / 2)\) (c) \(\tan ^{2}(z / 2)\) (d) \(\cot ^{2}(z / 2)\)
If \(4 \sin ^{-1} x+3 \cos ^{-1} x=2 \pi\), then \(x=\) (a) 1 (b) \(-1\) (c) \((1 / 2)\) (d) \(-(1 / 2)\)
\(\tan ^{-1}(\tan 4)-\tan ^{-1}(\tan (-6))+\cos ^{-1}(\cos 10)=\) (a) 16 (b) \(\pi\) (c) \(-\pi\) (d) \(5 \pi-12\)
\(\tan 20^{\circ}+4 \sin 20^{\circ}=\) (a) \((\sqrt{3} / 2)\) (b) \((1 / 2)\) (c) \(\sqrt{3}\) (d) \((1 / \sqrt{3})\)
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