JAMIA 2024 — Mathematics PYQ

Hume ${\cos }^{-1}(4x^3-3x)$ ka simplified form nikalna hai.

Step 1: Substitution (Maan lijiye)

Hum jaante hain ki $\cos (3\theta )$ ka formula niche diye gaye expression se milta-julta hai:

Isliye, hum $x=\cos \theta$ rakhte hain.

Yahan se, $\theta ={\cos }^{-1}x$ ho jayega.

Step 2: Value ko expression mein rakhein

Ab original expression mein $x$ ki jagah $\cos \theta$ rakhte hain:

Step 3: Formula apply karein

Upar diye gaye formula ka use karte hue:

Step 4: Simplify karein

Inverse property $({\cos }^{-1}(\cos (A))=A)$ ka use karke hume milta hai:

Step 5: $\theta$ ki original value wapas rakhein

Kyonki $\theta ={\cos }^{-1}x$ tha, isliye:

Final Answer:

${\cos }^{-1}(4x^3-3x)$ ka simplified form hai: