It is given that $\sin 25^\circ = \frac{a}{b}$. Express each of the following in terms of \(a

Question

It is given that $\sin 25^\circ = \frac{a}{b}$. Express each of the following in terms of $a$ and $b$. $\sin 25^\circ + \sin 45^\circ + \sin 65^\circ$ $\cos 25^\circ + \cos 45^\circ + \cos 65^\circ$ $\tan 205^\circ + \tan 225^\circ + \tan 245^\circ$ $\sec (-25^\circ) + \sec (-45^\circ) + \sec (-65^\circ)$

Accepted Answer

(i) $\dfrac{a + \sqrt{b^2 - a^2}}{b} + \dfrac{\sqrt{2}}{2}$; (ii) $\dfrac{a + \sqrt{b^2 - a^2}}{b} + \dfrac{\sqrt{2}}{2}$; (iii) $1 + \dfrac{b^2}{a \sqrt{b^2 - a^2}}$; (iv) $\sqrt{2} + \dfrac{b(a + \sqrt{b^2 - a^2})}{a \sqrt{b^2 - a^2}}$

Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

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