(b) Express \( \left(\sqrt{3} \cos \theta+\sin \theta\right. \) in the form \( R \cos (\theta-\alpha) \), where \( R>0 \) and \( 0^{\circ}<\alpha<90^{\circ} \). Hence, solve the equation \( \sqrt{3} \cos \theta+\sin \theta=-1,0^{\circ}<\theta<360^{\circ} \).

24. Prove that \( 1+\frac{\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta \)

find the fundamental periodicity of the following fonction \( y=-5 \sin \left(\frac{1}{4}(3-x)\right)+1 \)

11. if \( \cos \theta=\frac{3}{3}, \theta \in Q_{1} \) then \( \cot \theta+\operatorname{cosec} \theta= \) \( \begin{array}{llll}\text { a) } 1 & \text { b) } 25 & \text { c) } 3 & \text { d) } 4\end{array} \)

24. - Prove that \( 1+\frac{\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta \)

Define the secant function in terms of a right triangle.