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dinainjune
sin 17 = a so, cot 253+csc253 = ?
the choice is a. (a-1)/sqrt(1-a^2) b. (1-a) / sqrt (1-a^2) c. (a-1)/sqrt(a^2-1) d. (1-a) / sqrt (a^2-1) e. (-a-1) / sqrt (1-a^2)
(cos253+1)/sin253=(1+cos270cos17+sin270sin17)/(sin270in17-cos270cos17)=(1-a)/(-a)=1-1/a
the answer is b. (1-a)/sqrt(1-a^2) sin 17=a -> cos 253=cos 73=-a. Furthermore, cot 253 + csc 253 = (cos 253+1)/sin253 hence the answer
Notice that 270 - 253 = 17, so sin (17) = -cos (253) cot 253 + csc 253 = [cos(253)/sin(253)] + 1/sin(253) = [cos (253) + 1]/sin(253) but cos(253) = -a so: 1-a/sin(253) from the numerator, we know only b or d could be correct. Looking at the denominator, sin(253), we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1 Thus, sin(253) = sqrt[sin^2(253)] = sqrt[1-cos^2(253)] and -cos(253) is a, so the denominator is sqrt(1-a^2) The end equation is 1-a/sqrt(1-a^2) B is the correct answer