Question 4, Review Exercise

Solutions of Question 4 of Review Exercise of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the values of: $\dfrac{1+\tan 15^{\circ}}{1-\tan 15^{\circ}}$

Solution.

$$\begin{align*} &\frac{1+\tan 15^{\circ}}{1-\tan 15^{\circ}}\\ =&\frac{1+\tan 15^{\circ}}{1-1 \cdot \tan 15^{\circ}}\\ =&\frac{\tan 45^{\circ} + \tan 15^{\circ}}{1 - \tan 45^{\circ} \tan 15^{\circ}}\\ =& \tan(45^{\circ} + 15^{\circ})\\ =& \tan(60^{\circ})\\ =&1.732 \end{align*}$$

Find the values of: $\cos 70^{\circ} \cdot \cos 20^{\circ}-\sin 70^{\circ} \sin 20^{\circ}$

Solution.

$$\begin{align*} &\cos 70^{\circ} \cdot \cos 20^{\circ} - \sin 70^{\circ} \sin 20^{\circ} \\ =& \cos(70^{\circ} + 20^{\circ}) \\ =& \cos(90^{\circ}) \\ =& 0 \end{align*}$$

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