Question:
$\int\frac{dx}{sin^{2}x~cos^{2}x}=$
$\int\frac{dx}{sin^{2}x~cos^{2}x}=$
Show Hint
$\int sec^{2}x~dx = tan~x$ and $\int cosec^{2}x~dx = -cot~x$.
Updated On: Jun 19, 2026
- $tan~x+cot~x+c$
- $tan~x-cot~x+c$
- $tan~x~cot~x+c$
- $tan~x-cot~2x+c$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Use the trigonometric identity $1 = sin^{2}x + cos^{2}x$.
Step 2: Analysis
Replace the numerator $1$ with the identity:
$\int\frac{sin^{2}x + cos^{2}x}{sin^{2}x~cos^{2}x}dx = \int(\frac{sin^{2}x}{sin^{2}x~cos^{2}x} + \frac{cos^{2}x}{sin^{2}x~cos^{2}x})dx$
Step 3: Calculation
$\int(sec^{2}x + cosec^{2}x)dx = tan~x - cot~x + c$.
Step 4: Conclusion
Hence, the correct answer is $tan~x - cot~x + c$. Final Answer: (B)
Use the trigonometric identity $1 = sin^{2}x + cos^{2}x$.
Step 2: Analysis
Replace the numerator $1$ with the identity:
$\int\frac{sin^{2}x + cos^{2}x}{sin^{2}x~cos^{2}x}dx = \int(\frac{sin^{2}x}{sin^{2}x~cos^{2}x} + \frac{cos^{2}x}{sin^{2}x~cos^{2}x})dx$
Step 3: Calculation
$\int(sec^{2}x + cosec^{2}x)dx = tan~x - cot~x + c$.
Step 4: Conclusion
Hence, the correct answer is $tan~x - cot~x + c$. Final Answer: (B)
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Integration Questions
- Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
- Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]
- Evaluate the integral: \[ \int \frac{\sin x}{\sin\left(x-\frac{\pi}{4}\right)}\,dx \]
- Evaluate the integral: \[ \int_0^{\frac{\pi}{2}} \frac{dx}{1 + \cos x} \]
- Evaluate the integral: \[ \int \left[ \frac{1 - \log x}{1 + (\log x)^2} \right]^2 dx \]
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions