Question:
If \( \cosec\theta + \cot\theta = 5 \), then \( \sin\theta = \)
If \( \cosec\theta + \cot\theta = 5 \), then \( \sin\theta = \)
Show Hint
Whenever expressions involve \( \cosec\theta \) and \( \cot\theta \), multiplying by their conjugate simplifies calculations.
Updated On: Mar 28, 2026
- \( \dfrac{1}{5} \)
- \( \dfrac{5}{26} \)
- \( \dfrac{5}{13} \)
- \( \dfrac{1}{13} \)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use the identity.
\[ (\cosec\theta + \cot\theta)(\cosec\theta - \cot\theta) = 1 \] Step 2: Find \( \cosec\theta - \cot\theta \).
\[ \cosec\theta - \cot\theta = \frac{1}{5} \] Step 3: Solve the system.
\[ \cosec\theta + \cot\theta = 5 \] \[ \cosec\theta - \cot\theta = \frac{1}{5} \] Adding, \[ 2\cosec\theta = \frac{26}{5} \Rightarrow \cosec\theta = \frac{13}{5} \] Step 4: Find \( \sin\theta \).
\[ \sin\theta = \frac{5}{13} \] Step 5: Conclusion.
The value of \( \sin\theta \) is \( \dfrac{5}{13} \).
\[ (\cosec\theta + \cot\theta)(\cosec\theta - \cot\theta) = 1 \] Step 2: Find \( \cosec\theta - \cot\theta \).
\[ \cosec\theta - \cot\theta = \frac{1}{5} \] Step 3: Solve the system.
\[ \cosec\theta + \cot\theta = 5 \] \[ \cosec\theta - \cot\theta = \frac{1}{5} \] Adding, \[ 2\cosec\theta = \frac{26}{5} \Rightarrow \cosec\theta = \frac{13}{5} \] Step 4: Find \( \sin\theta \).
\[ \sin\theta = \frac{5}{13} \] Step 5: Conclusion.
The value of \( \sin\theta \) is \( \dfrac{5}{13} \).
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 Trigonometry Questions
- The value of \( \sin(\cot^{-1}(x)) \) is:
- If \( \sin^{-1} x + \cos^{-1} y = \frac{3\pi}{10} \), then the value of \( \cos^{-1} x + \sin^{-1} y \) is:
- \( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
- One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:
- If \(\alpha + \beta = \frac{\pi}{2}\) and \(\beta + \gamma = \alpha\), then the value of \(\tan\alpha\) is:
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