Question : The value of $\frac{\operatorname{sin} 58^{\circ}}{\cos 32^{\circ}}+\frac{\sin 55^{\circ} \sec 35^{\circ}}{\tan 5^{\circ} \tan 45^{\circ} \tan 85^{\circ}}$ is equal to:

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: 3

Question : The value of the expression $\sin^{2}1^{\circ}+\sin^{2}11^{\circ}+\sin^{2}21^{\circ}+\sin^{2}31^{\circ}+\sin^{2}41^{\circ}+\sin^{2}45^{\circ}+\sin^{2}49^{\circ}+\sin^{2}59^{\circ}+\sin^{2}69^{\circ}+\sin^{2}79^{\circ}+\sin^{2}89^{\circ}$ is:

Option 1: $0$

Option 2: $5\frac{1}{2}$

Option 3: $5$

Option 4: $4\frac{1}{2}$

Question : What is the value of $\frac{4}{3}\left(\sin ^2 35^{\circ}+\sin ^2 55^{\circ}\right) ?$

Option 1: $\frac{2}{3}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{8}{9}$

Option 4: $\frac{3}{4}$

Question : The value of $\frac{\sin 25^{\circ}\cos 65^{\circ}+\cos 25^{\circ}\sin 65^{\circ}}{\tan ^{2}70^{\circ}-cosec^{2}20^{\circ}}$ is:

Option 1: –1

Option 2: 0

Option 3: 1

Option 4: 2

Question : Find the value of $\frac{\cos^{2}25^\circ-\sin^{2}65^\circ}{\cos^{2}25^\circ+\sin^{2}65^\circ}$

Option 1: $\frac{1}{2}$

Option 2: $1$

Option 3: $–1$

Option 4: $0$