Let x=sinα,y=sinβ. The equation becomes cosα+cosβ=a(sinα−sinβ). Using sum-to-product, this simplifies to cot2α−β=a. So sin−1x−sin−1y= constant. Differentiating: 1−x21−1−y21dxdy=0, giving dxdy=1−x21−y2.
CUET UG 2023 — Mathematics Calculus
If 1−x2+1−y2=a(x−y), then dxdy=
Held on 25 May 2023 · Verified 13 Jul 2026.
1−y21−x2
1−x21−y2
1+y21−x2
1−y21+x2
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
The derivative of x³ + 2x² - 5x + 1 is:
The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is:
If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct? (A) $a = 3$ (B) $a = -3$ (C) $b = 12$ (D) $b = -12$ Choose the correct answer from the options given below:
The function $f(x) = kx^3 + 6kx^2 + 18x + 17$ is increasing on $\mathbb{R}$(set of real numbers) if:
Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :
Work through every CUET UG Calculus PYQ, year by year.