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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 20 of 61
Marks: +1, -0
cos⁡2π6+csc⁡5π6+3tan⁡2π6\cos^2\frac{\pi}{6}+\csc\frac{5\pi}{6}+3\tan^2\frac{\pi}{6} = 6
Solution:  
L.H.S. = cos⁡2π6+csc⁡5π6+3tan⁡2π6\cos^2\frac{\pi}{6}+\csc\frac{5\pi}{6}+3\tan^2\frac{\pi}{6}
= (3)2\left(\sqrt{3}\right)^2 + cosec (6π−π6)\left(\frac{6\pi-\pi}{6}\right) + 3 (13)2\left(\frac{1}{\sqrt{3}}\right)^2
= 3 + cosec (π−π6)\left(\pi-\frac{\pi}{6}\right) + 3 × 13\frac{1}{3} = 3 + cosec π6\frac{\pi}{6} + 1 = 3 + 2 + 1 = 6 = R.H.S.
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