Trigonometric Identities and Formulae
Question 2
Given that $\sin \left( A+B \right)=2\sin \left( A-B \right)$, evaluate $\frac{\tan B}{\tan A}$.
Question 3
2022 PSS AM S4 P1 Q10
(a)
Prove the identity $\frac{\cos \theta }{1-\sin \theta }+\frac{1-\sin \theta }{\cos \theta }=2\sec \theta $.
[4]
(b)
Hence solve the equation $\frac{\cos 3\beta }{1-\sin 3\beta }+\frac{1-\sin 3\beta }{\cos 3\beta }=4$ for $0{}^\circ \le \beta \le 180{}^\circ $.
[5]
(a)
(b)
Question 4
2022 CGS AM S4 P2 Q4
In the diagram, $DFGE$ is a rectangle and triangle $ABC$ is an isosceles with $AB=AC=5$m.
$ADB$ and $AEC$ are straight lines. $DE$ is parallel to $BC$ and $AB=4AD$. Angle $ABC=\theta $ where ${{0}^{\circ }}<\theta <{{90}^{\circ }}$.
(a)
Show that the perimeter, $P$ metres, of rectangle $DFGE$ is give $P=\frac{5}{2}\left( 2\cos \theta +3\sin \theta \right)$.
[3]
(b)
Express $P$ in the form $\frac{5}{2}R\cos \left( \theta -\alpha \right)$, where $R>0$ and write down the largest possible value of $P$.
[3]
(c)
Find the value of $\theta $ for which $P=6$.
[3]
(a)
(b)
(c)
