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a)Solve for ?, if tan5? = 1.
Ans: Tan 5? = 1 ⇒ ? =45/5 ⇒ ?=9o.
b)Solve for ? if Sin?/1 + Cos? + 1 + Cos?/ Sin? = 4 .
Ans: Sin?/1 + Cos? + 1 + Cos?/ Sin? = 4
Sin2?/1 + 1 (Cos?)2/ Sin?(1 + Cos?) = 4
Sin2?+1 + Cos2? + 2cos?/ Sin? +Sin?Cos? = 4
2 +2Cos? / Sin?(1+ cos?) =4
2+(1+ cos?)/Sin?(1+ cos?) = 4
2/sin? = 4
sin ? = 1/2
sin ? = sin 30
? = 30o
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Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
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