(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 \( 1+\frac{\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta \)

119. If \( A=30^{\circ} \), then show that: \( V 2 \) (i) \( \sin \left(60^{\circ}+A\right)-\sin \left(60^{\circ}-A\right)=\sin A \)

6) а) Решите уравнение \( \frac{2022^{\cos 2 x}-2022^{\cos x}}{\sqrt{-2021 \sin x}}=0 \). б) Укажите корни этого уравнения, принадлежащие отрезку \( \left[-\frac{11 \pi}{2} ;-\frac{9 \pi}{2}\right] \).

\( \sin \alpha - i \cos \alpha \)

यदी \( \tan \theta 1 \) तो \( 2 \sin \theta \cos \theta \) का मान जे ज्ञात किजिए