MCQ
$\int_{}^{} {\frac{{\cos 2x - \cos 2\alpha }}{{\cos x - \cos \alpha }}} dx = $
- ✓$2[\sin x + x\cos \alpha ] + c$
- B$2[\sin x + \sin \alpha ] + c$
- C$2[ - \sin x + x\cos \alpha ] + c$
- D$ - 2[\sin x + \sin \alpha ] + c$
✓
Answer
Correct option: A.
$2[\sin x + x\cos \alpha ] + c$
a
(a)$\int_{}^{} {\frac{{\cos 2x - \cos 2\alpha }}{{\cos x - \cos \alpha }}} \,dx = \int_{}^{} {\frac{{2({{\cos }^2}x - {{\cos }^2}\alpha )}}{{\cos x - \cos \alpha }}\,dx} $
$ = 2\int_{}^{} {(\cos x + \cos \alpha )\,dx} = 2(\sin x + x\cos \alpha )$.
(a)$\int_{}^{} {\frac{{\cos 2x - \cos 2\alpha }}{{\cos x - \cos \alpha }}} \,dx = \int_{}^{} {\frac{{2({{\cos }^2}x - {{\cos }^2}\alpha )}}{{\cos x - \cos \alpha }}\,dx} $
$ = 2\int_{}^{} {(\cos x + \cos \alpha )\,dx} = 2(\sin x + x\cos \alpha )$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If a line makes angles $\alpha,\beta,\gamma$ with the axis then $\cos 2\alpha+ \cos 2\beta +\cos 2\gamma=$
→Three numbers are chosen at random without replacement from :$\{1,2,3,4,5,6,7,8\}$. The probability that their minimum is $3,$ given that their maximum is $6$, is :
→If A and B are two events such that $\text{P(A)}=\frac{3}{8},\text{P(B)}=\frac{5}{4}.$ and $\text{P}(\text{A}|\text{B})\times\text{P}(\overline{\text{A}}\cap\text{B})$ is equals to.
→$\int_{\,1}^{\,3} {(x - 1)(x - 2)(x - 3)dx = } $
→Let $X$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. What are possible values of $X\ ?$
→If $x + y = 3$ and $xy = 2,$ then the value of $x^3 - y^3$ is equal to.
→Choose the correct option from given four options:
$\frac{\text{dx}}{\sin(\text{x}-\text{a})\sin(\text{x}-\text{b})}$ is equal to:
→$\frac{\text{dx}}{\sin(\text{x}-\text{a})\sin(\text{x}-\text{b})}$ is equal to:
The value of $\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\big(\text{x}^3+\text{x}\cos\text{x}+\tan^5\text{x}+1\big)\text{dx},$ is:
→If $f$ be a polynomial, then the second derivative of $f({e^x})$ is
→The maximum value of $Z=5 x+3 y$, if the shaded region represents the feasible region, is
→