evaluate cos 39 deg/sin51deg + 3 tan 13 deg tan 29 deg tan 45 deg tan 77 deg tan 61 deg- 2 (cos sq31 deg +cos sq59 deg)

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Solution

$\frac{\cos 39 °}{\sin 51 °} + 3 \tan 13 ° \tan 29 ° \tan 45 ° \tan 77 ° \tan 61 ° - 2 (\cos^{2} 31 ° + \cos^{2} 59 °) = \frac{\cos (90 - 51) °}{\sin 51 °} + 3 \tan (90 - 77) ° \tan (90 - 61) ° \tan 45 ° \tan 77 ° \tan 61 ° - 2 (\cos^{2} (90 - 59) ° + \cos^{2} 59 °) = \frac{\sin 51 °}{\sin 51 °} + 3 \cot 77 ° \cot 61 ° \tan 45 ° \tan 77 ° \tan 61 ° - 2 (\sin^{2} 59 ° + \cos^{2} 59 °) (Since \cos (90 - x) = \sin x and \tan (90 - x) = \cot x) = 1 + 3 \tan 45 ° - 2 (Since \sin^{2} x + \cos^{2} x = 1) = 1 + 3 - 2 = 2 ANS . . .$

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