\( \alpha=90^{\circ}, \beta=30^{\circ} \) হলে, \( \sin (\alpha-\beta) \)-এর মান \( \begin{array}{llll}\text { (a) } 1 & \text { (b) } \frac{1}{2} & \text { (c) } \frac{\sqrt{3}}{2} & \text { (d) } \frac{1}{\sqrt{2}}\end{array} \)

a) \( \sin ^{4} x+\cos ^{2} x \cdot \sin ^{2} x-\sin ^{2} x \)

The angle of depression from one mountain summit to another is \( 15.9^{\circ} \). If the two mountains differ in height by 430 metres, find the horizontal distance between the two summits, to the nearest centimetre.

5. Reducir: \[ L=\operatorname{sen} x(\csc x+\operatorname{sen} x)+\cos x(\sec x+\cos x)+1 \] \( \begin{array}{lll}\text { a) } 1 & \text { b) } 2 & \text { c) } 3 \\ \text { d) } 4 & \text { e) } 5 & \text { c) }\end{array} \)

- \( \left|\begin{array}{l}\text { 1.Решите уравнение. В ответе напишите } \\ \text { наименьший положительный корень. } \\ \sin \frac{\pi(x+9)}{4}=-1\end{array}\right| \)

2. Решите уравнение . В ответе напишите наименьший положительный корень. \( \sin \frac{\pi(4 x-3)}{4}=\frac{\sqrt{2}}{2} \)