JAMIA 2024 — Mathematics PYQ

Solution:

Hume iska maan (value) nikalna hai:

Step 1: Formula ka use karein

Hum jaante hain ki:

(Yahan xy < 1 hona chahiye. Is case mein \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} < 1, isliye yeh formula valid hai.)

Step 2: Values ko formula mein rakhein

Yahan $x=\frac{1}{2}$ aur $y=\frac{1}{3}$ rakhne par:

Step 3: Numerator (ansh) aur Denominator (har) ko simplify karein

Numerator: $\frac{1}{2}+\frac{1}{3}=\frac{3+2}{6}=\frac{5}{6}$

Denominator: $1-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}$

Ab in values ko wapas expression mein rakhte hain:

Step 4: Final value nikaalein

Hum jaante hain ki $\tan (\frac{\pi }{4})=1$, isliye:

Final Answer:

${\tan }^{-1}\left(\frac{1}{2}\right)+{\tan }^{-1}\left(\frac{1}{3}\right)$ ki value hai: