Question:
Solve:
\[
\int \frac{\sin x}{\sin (x+a)} \, dx.
\]
Solve:
\[ \int \frac{\sin x}{\sin (x+a)} \, dx. \]Show Hint
Use trigonometric identities to simplify integrals involving sine and cosine.
Updated On: Mar 3, 2025
Show Solution
Verified By Collegedunia
Solution and Explanation
We use the substitution:
\[
I = \int \frac{\sin x}{\sin (x+a)} dx.
\]
Using the identity:
\[
\sin (x+a) = \sin x \cos a + \cos x \sin a,
\]
we express the integral in a solvable form and integrate accordingly.
Was this answer helpful?
0
0
Top UP Board XII Mathematics Questions
- (c) Solve the differential equation \( (\tan^{-1} y - x) dy = (1 + y^2) dx \):
- (d) If \( (\cos x)^y = (\cos y)^x \), find \( \frac{dy}{dx} \):
- (e) If \( y = x \cos (a + y) \) and \( \cos a \neq \pm 1 \), prove that \[ \frac{dy}{dx} = \frac{\cos^2 (a + y)}{\sin a}. \]
- (a) If a die is thrown three times, find the probability of getting one appearing number in them will be odd:
- (b) Minimize \( Z = x + 2y \) under the following constraints: \[ 2x + y \geq 3, \quad x + 2y \geq 6, \quad x \geq 0, \quad y \geq 0. \]
View More Questions
Top UP Board XII Integration Questions
- (c) Solve: \[ \int \frac{3x + 5}{x^3 - x^2 - x + 1} \, dx. \]
- (a) Prove that: \[ \int_{0}^{\frac{\pi}{2}} \frac{x \sin x}{1 + \cos^2 x} \, dx = \frac{\pi^2}{4}. \]
- (b) Find the value of: \[ \int_{0}^{\frac{\pi}{2}} \frac{x \, dx}{a^2 \cos^2 x + b^2 \sin^2 x}. \]
- (b) The value of \( \int x \sin x \, dx \) will be:
- (c) If \( 2P(A) = P(B) = \frac{5}{13} \) and \( P(A \mid B) = \frac{2}{5} \), then find \( P(A \cap B) \).
View More Questions
Top UP Board XII Questions
- In which one of the following States of India is the density of population the highest?
- Which one of the following States of India has the largest urban population?
- Which one of the following States is not related to the production of mineral oil?
- Which one of the following sea ports is located on the eastern coast of India?
- What is meant by ‘Humanisation of Nature’?
View More Questions