If tan(t) + cot(t) = 1, then one of the values of the expression 1/[sin(t)+cos(t)] is.
tan(t) + cot(t) = 1, sin(t)/cos(t) + cos(t) /sin(t) = 1 sin²(t) + cos²(t) = sin(t) cos(t) sin(t) cos(t)= 1 … (1) Squaring sin(t) + cos(t), (sin(t) + cos(t)) ² = 1 + 2 sin(t) cos(t) = 1 + 2 × 1 = 3 sin(t) + cos(t) = √3 Thus, 1/ sin(t) + cos(t) = 1 /√3 = =1 /√3.
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