cos A = 0.6; sin A = √ (1 – cos ^ 2 A) = √ (1 – 0.6 ^ 2) = √ (1 – 0.36) = √0.64) = 0.8;
Now we express the values of sin A and cos A in terms of sin B and cos B, taking into account that (A + B) = 90.
sin A = cos (90 – A) = cos B; cos A = sin (90 – A) = sin B, then the sought-for tg B * ctg A = (sin B / cos B) * (cos A / sin A) = (cos A / sin A) * (cos A / sin A) = (0.6 / 0.8) ^ 2 = (3/4) ^ 2 = 9/16.
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