## Trigonometry (11th Edition) Clone

Write $\tan87^\circ$ in terms of the cofunction of the complementary angle: $$\cot3^\circ$$
$$\tan87^\circ$$ Cotangent is the cofunction of tangent. That means the question asks to write $\tan87^\circ$ in terms of cotangent and an angle. In other words, what is $\theta$ with which $$\cot\theta=\tan87^\circ\hspace{1cm}(1)$$ According to Cofunction Identity: $\cot\theta=\tan(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\tan(90^\circ-\theta)=\tan87^\circ$$ $$90^\circ-\theta=87^\circ$$ $$\theta=90^\circ-87^\circ=3^\circ$$ Therefore $\cot3^\circ$ is the answer.