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CBSE Class 12 Math 2020 Outside Delhi Set 3 Solved Paper

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Note : Except for the following questions, all the remaining questions have been asked in the previous sets.
SECTION - A
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Question : 1 of 11
Marks: +1, -0
The value of tan⁡−1[12cos⁡−1(53)]\tan^{-1} \left[ \frac{1}{2} \cos^{-1} \left( \frac{\sqrt{5}}{3} \right) \right] is
Solution:     👈: Video Solution
y=tan⁡[12cos⁡−1(53)]y = \tan \left[ \frac{1}{2} \cos^{-1} \left( \frac{\sqrt{5}}{3} \right) \right]
Let, x=cos⁡−1(53)x = \cos^{-1} \left( \frac{\sqrt{5}}{3} \right)
⇒cos⁡x=53\Rightarrow \cos x = \frac{\sqrt{5}}{3}
∴y=tan⁡12x\therefore y = \tan \frac{1}{2} x
y=tan⁡x2y = \tan \frac{x}{2}
y=1−cos⁡x1+cos⁡xy = \sqrt{\frac{1-\cos x}{1+\cos x}}
=1−531+53= \sqrt{\frac{1-\frac{\sqrt{5}}{3}}{1+\frac{\sqrt{5}}{3}}}
=3−53+5= \sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}
rationalizing the factor, we get,
y=3−52y = \frac{3-\sqrt{5}}{2}
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