If 3 x + 4 x = 5, then 4 x - 3 x = - Vidyadip

MCQ

If $3 \sin x + 4 \cos x = 5,$ then $4 \sin x - 3 \cos x =$

A
$1$
B
$5$
C
$3$
✓
$0$

✓

Answer

Correct option: D.

$0$

$\frac{3}{5} \sin x+\frac{4}{5} \cos x=1$
Let $\cos \alpha=\frac{3}{5}$ and $\sin \alpha=\frac{4}{5}$
$\therefore \cos \alpha \sin x+\sin \alpha \cos x=1$
$\Rightarrow \sin (\alpha+x)=\sin \frac{\pi}{2}$
$\Rightarrow \alpha+x=\pi$
$\Rightarrow x=\frac{\pi}{2}-\alpha \ldots . \text { (i) }$
We have to find the value of $4 \sin x - 3 \cos x$
$4 \sin \left(\frac{\pi}{2}-\alpha\right)-3 \cos \left(\frac{\pi}{2}-\alpha\right) \ldots$ From eq. $(i)$
$=4 \cos \alpha-3 \sin \alpha$
$=4 \times \frac{3}{5}-3 \times \frac{4}{5}\left(\because \cos \alpha=\frac{3}{5} \text { and } \sin \alpha=\frac{4}{5}\right)$
$0$

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 "M.C.Q (1 Marks)" from Model Paper 8→Model Paper 8 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\sin x}} - 1}}{x} = $

If $P(x_1, y_1)$ and $Q(x_2, y_2)$ are points on $2x + 3y + 1 = 0$ such that $|PA - PB|$ is maximum and $|QA - QB|$ is minimum, where $A(2,0)$ and $B(0,2)$, then value of $x_1 - y_1 + x_2 - y_2 $ is -

Consider a triangle having vertices $A(-2,3), B(1,9)$ and $C(3,8)$. If a line $L$ passing through the circum-center of triangle $\mathrm{ABC}$, bisects line $\mathrm{BC}$, and intersects $\mathrm{y}$-axis at point $\left(0, \frac{\alpha}{2}\right)$, then the value of real number $\alpha$ is $.....$

The locus of $z$ satisfying the inequality ${\log _{1/3}}|z + 1|\, > $ ${\log _{1/3}}|z - 1|$ is

Let $P$ be the point on the parabola ${y^2} = 8x$ which is at a minimun distance from the centre $C$ of the circle ${x^2} + {\left( {y + 6} \right)^2} = 1$ . Then the equation of the circle , passing through $C$ and having its centre at $P $ is :

If the expansion in powers of $x$ of the function $\frac{1}{{\left( {1 - ax} \right)\left( {1 - bx} \right)}}$ is ${a_0} + {a_1}x + {a_2}{x^2} + \;{a_3}{x^3} + \; \ldots......$ then ${a_n}$ is

"If Deb and Sam go to the mall then it is snowing"
Which statement below is logically equivalent?

$n (n+1) (n+5)$ is a multiple of $3$ is true for

If the digits are not allowed to repeat in any number formed by using the digits $0,2,4,6,8$, then the number of all numbers greater than $10,000$ is equal to $....$

If $A = sin\, 45^o + cos\, 45^o$ and $B = sin\, 44^o + cos\, 44^o $, then