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Kindly refer table above for different trigonometric identities.
(3 cos 55) / (7 sin 35) -( 4( cos 70 csc 20))/(7(tan 5 tan 25 tan 45 tan 65 tan 85))
=> ((3 cos 55) / (7 sin (90 - 55)) )- ((4 cos 70 * (1/ sin 20)) / (7 (tan 5 * tan 25 * tan 45 * tan (90 - 25) * tan(90 - 5))))
From table we know, sin (90 - theta) = cos theta, tan (90-theta) = cot theta, csc theta = 1/ sin theta, tan theta * cot theta = 1
=> ((3 cancel(cos 55)) / (7 cancel(cos 55))) - ((4 cos 70 / sin (90-70))/(7(cancel(color(green)(tan 5 )) * cancel(color(blue)(tan 25 )) * tan 45 * cancel(color(blue)(cot 65) )* cancel(color(green)(cot 5))))
(3/7) - ((4 color(brown)(cancel(cos 70) )* 1/(color(brown)cancel(cos 70))) / (7 cancel(tan 45)^color(red)1)) as tan 45 = 1
=> = 3/ 7- 4 / 7 = color(purple)(-1/7
