CUET UG 2025 — Mathematics Arithmetic

The angle with tangent value of 1 occurs when opposite = adjacent, which happens at 45° or $\frac{\pi}{4}$4π​ radians.

$$\tan^{-1}(1) = \frac{\pi}{4}$$tan−1(1)=4π​

---

For cosine value of $-\frac{\sqrt{3}}{2}$−23​​, the negative sign indicates the 2nd or 3rd quadrant. The range of inverse cosine is $[0, \pi]$[0,π], so the 2nd quadrant is used.

Since $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$cos(6π​)=23​​

In the 2nd quadrant:

$$\pi - \frac{\pi}{6} = \frac{5\pi}{6}$$π−6π​=65π​

$$\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) = \frac{5\pi}{6}$$cos−1(−23​​)=65π​

---

The sine value of $\frac{1}{2}$21​ is a standard value:

$$\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$$sin(6π​)=21​

$$\sin^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{6}$$sin−1(21​)=6π​

---

Adding all three values:

$$\frac{\pi}{4} + \frac{5\pi}{6} + \frac{\pi}{6}$$4π​+65π​+6π​

Converting to common denominator of 12:

$$\frac{3\pi}{12} + \frac{10\pi}{12} + \frac{2\pi}{12}$$123π​+1210π​+122π​

$$= \frac{15\pi}{12}$$=1215π​

$$= \frac{5\pi}{4}$$=45π​

Therefore, the value is $\frac{5\pi}{4}$45π​.