Download App

3. trignometrical ratios,functions and identities — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS3. trignometrical ratios,functions and identities1 Mark
MCQ
$3\,\left[ {{{\sin }^4}\,\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}\,(3\pi + \alpha )} \right]$ $ - 2\,\left[ {{{\sin }^6}\,\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right] = $
  • A
    $0$
  • ✓
    $1$
  • C
    $3$
  • D
    $\sin \,4\alpha + \sin \,6\alpha $
✓

Answer

Correct option: B.
$1$
b
(b) $3\left\{ {{{\sin }^4}\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}(3\pi + \alpha )} \right\}$
$ - 2\left\{ {{{\sin }^6}\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right\}$
$ = 3\left\{ {\,{{( - \cos \alpha )}^4} + {{( - \sin \alpha )}^4}} \right\} - 2\,\left\{ {{{\cos }^6}\alpha + {{\sin }^6}\alpha } \right\}$
$ = 3\left\{ {{{\cos }^2}\alpha + {{\sin }^2}\alpha {)^2} - 2{{\sin }^2}\alpha {{\cos }^2}\alpha } \right\}$
$ - 2\left\{ {{{({{\cos }^2}\alpha + {{\sin }^2}\alpha )}^3} - 3{{\cos }^2}\alpha {{\sin }^2}\alpha ({{\cos }^2}\alpha + {{\sin }^2}\alpha )} \right\}$
$ = 3 - 6{\sin ^2}\alpha {\cos ^2}\alpha - 2 + 6{\sin ^2}\alpha {\cos ^2}\alpha = 3 - 2 = 1$
Trick : Put $\alpha = 0,\frac{\pi }{2},$ the value of expression remains $1$ i.e., it is independent of $\alpha $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\cos^2\Big(\frac{\pi}{6}+\text{x}\Big)-\sin^2\Big(\frac{\pi}{6}-\text{x}\Big)$ is:
→
Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $l$ and $II$ scoring a hit correctlyare $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
→
Latus rectum of ellipse $4{x^2} + 9{y^2} - 8x - 36y + 4 = 0$ is
→
If $\cos x + {\cos ^2}x = 1,$ then the value of ${\sin ^2}x + {\sin ^4}x$ is
→
The sum of the series ${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^{^2}} + {2.6^2} + .... + 2{(2m)^2}$ is
→
The point of intersection of the normals to the parabola $y^ 2\, = 4x$ at the ends of its latus rectum is 
→
The area of a parallelogram formed by the lines $ax \pm by \pm c = 0$, is
→
Choose the correct answer: Which of the following statement is a conjunction?
→
Which of the following proposition is a tautology?
→
$ABC$ is an isosceles triangle inscribed in a circle of radius $r$ . If $AB = AC $ $\& h$ is the altitude from $A$ to $BC$ and $P$ be the perimeter of $ABC$ then $\mathop {lim}\limits_{h \to 0} $ $\frac{\Delta }{{{P^3}}}$ equals (where $\Delta$ is the area of the triangle)
→