CUET PG 2023 — Mathematics PYQ

Step 1: Logarithm ki Property apply karna

Humein pata hai ki $log(A)+log(B)+log(C)=log(A\cdot B\cdot C)$. Is property ko sequence par lagane par:

Step 2: Trigonometric Identity ka use

Humein pata hai ki $\tan (90^{\circ }-\theta )=\cot \theta$. Iska matlab hai:

• $\tan 89^{\circ }=\tan (90^{\circ }-1^{\circ })=\cot 1^{\circ }$

• $\tan 88^{\circ }=\tan (90^{\circ }-2^{\circ })=\cot 2^{\circ }$

• Aur isi tarah baaki terms ke liye bhi.

Saath hi, $\tan \theta \cdot \cot \theta =1$ hota hai.

Step 3: Terms ko pair karna

Ab hum product ke andar terms ko pairs mein arrange karte hain:

Substitutions ke baad:

Humein pata hai ki har pair ka product 1 hoga aur $\tan 45^{\circ }$ ki value bhi 1 hoti hai.

Step 4: Final Calculation

Product simplify hokar $1$ reh jayega:

Kyunki kisi bhi base par $log(1)$ ki value 0 hoti hai:

Answer: Is expression ki value 0 hai.