using trigonometrical identities
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numerator sin 35 cos 55 + cos 35 sin 55 represents the formula of sin a + b is sin a cos b + cos a sin b. so add sin 35 + 55 equals to sin 90 so the numerator is one. convert co secant 10 into secant 80 by converting 10 as 90 - 80. so the denominator now becomes second square 80 - 10 square 80 which is equals to 1. no problem one by one becomes one. so the solution is 1
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