Question

If tan 2theta= cot(theta+6) where (2theta) and (theta+6) are acute angles the find the value of theta

Answer 1

Dear Student,

$$\begin{gathered} \tan 2\mathrm{\theta }=\cot \left(\mathrm{\theta }+6\right) \\ \cot \left(90-2\mathrm{\theta }\right)=\cot \left(\mathrm{\theta }+6\right)\left(\mathrm{Since}\cot \left(90-\mathrm{\theta }\right)=\tan \mathrm{\theta }\right) \\ 90-2\mathrm{\theta }=\mathrm{\theta }+6 \\ 90-6=\mathrm{\theta }+2\mathrm{\theta } \\ 84=3\mathrm{\theta } \\ \mathrm{\theta }=\frac{84}{3} \\ \mathrm{\theta }=28°\mathrm{ANS}... \end{gathered}$$

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