Question : What is the value of $\text{cosec}15°\sec 15°?$
Option 1: 0.5
Option 2: 4
Option 3: 2
Option 4: 1
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Correct Answer: 4
Solution : $\text{cosec}15°\sec 15°$ $=\frac{1}{\sin 15°}\frac{1}{\cos 15°}$ Multiplying and dividing by 2, we get ⇒ $\frac{2}{2\sin 15° \cos 15°}$ $= \frac{2}{\sin30°}$ $= \frac{2}{\frac{1}{2}}$ $= 2\times 2 = 4$ Hence, the correct answer is 4.
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Question : The value of $\text{cot 17°}(\text{cot 73°} \cos^{2}22°+\frac{1}{\cot 17°\sec^{2}68°})$ is:
Option 1: $0$
Option 2: $1$
Option 3: $2$
Option 4: $\sqrt{3}$
Question : If $\sec( 4x-50°)=\operatorname{cosec}( 50°-x)$, then the value of $x$ is:
Option 1: 45°
Option 2: 90°
Option 3: 30°
Option 4: 60°
Question : What is the value of $\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$?
Option 1: $2$
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\sqrt{2}$
Option 4: $\frac{1}2$
Question : If $\sec 2 \theta=\operatorname{cosec}(\theta-36°)$, where $2 \theta$ is an acute angle, find the value of $\theta$.
Option 1: 32°
Option 2: 46°
Option 3: 20°
Option 4: 42°
Question : The value of $\operatorname{cosec}^{2}60°+\sec^{2}60°– \cot^{2}60°+\tan^{2}30°$ will be:
Option 1: $5$
Option 2: $5\frac{1}{2}$
Option 3: $5\frac{1}{3}$
Option 4: $5\frac{2}{3}$
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