If $\displaystyle \tan 32^0.\cot (90^0-\theta )=1$ find $\theta $.
- $\displaystyle 58^{\circ}$
- $\displaystyle 122^{\circ}$
- $\displaystyle 32^{\circ}$
- $\displaystyle 158^{\circ}$
Reveal answer
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A
Correct answer
Explanation
tan(32) * cot(90 - theta) = 1. Since cot(90 - theta) = tan(theta), we have tan(32) * tan(theta) = 1. This implies tan(theta) = 1/tan(32) = cot(32) = tan(90 - 32) = tan(58). Thus, theta = 58 degrees.
AI explanation
First, apply the complementary angle identity to simplify cot(90 degrees minus theta) to tan theta. The equation becomes tan 32 degrees multiplied by tan theta equals 1, which implies tan theta equals cot 32 degrees. Using the complementary identity again, cot 32 degrees equals tan 58 degrees, giving theta equals 58 degrees.