Question : If $3 \sin x+4 \cos x=2$, then the value of $3 \cos x – 4 \sin x$ is equal to:
Option 1: $\sqrt{23}$
Option 2: $\sqrt{21}$
Option 3: $\sqrt{29}$
Option 4: $21$
Latest: SSC CGL Tier 1 Result 2024 Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: $\sqrt{21}$
Solution : Given: $3 \sin x+4 \cos x=2$ (equation 1) Let $3 \cos x–4 \sin x=k$ (equation 2) We know the trigonometric identity, $\sin^2 x+ \cos^2 x=1$. Squaring the equation and adding them together, $(3 \cos x–4 \sin x)^2+(3 \sin x+4 \cos x)^2=k^2+2^2$ ⇒ $9 \cos^2 x+16 \sin^2 x–24\sin x \cos x+9 \sin^2 x+16 \cos^2 x+24 \sin x \cos x=k^2+4$ ⇒ $9( \cos^2 x+ \sin^2 x)–24\sin x \cos x+16 (\sin^2 x+ \cos^2 x)+24 \sin x \cos x=k^2+4$ ⇒ $9+16=k^2+4$ ⇒ $25=k^2+4$ ⇒ $25–4=k^2$ ⇒ $k^2=21$ ⇒ $k=\sqrt{21}$ The value of $3 \cos x–4 \sin x=\sqrt {21}$. Hence, the correct answer is $\sqrt {21}$.
Candidates can download this ebook to know all about SSC CGL.
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Question : If $\cos x+\sin x=\sqrt{2} \cos x$, what is the value of $(\cos x-\sin x)^2+(\cos x+\sin x)^2$?
Question : If $\tan x = \frac{7}{5}$, the value of $\frac{9 \sin x – \frac{42}{5} \cos x}{15 \sin x + 21 \cos x}$ is:
Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:
Question : If $\sin (x+y) = \cos (x–y)$, then the value of $\cos^2 x$ is:
Question : In $\triangle{XYZ}$, right-angled at $Y$, if $\sin X = \frac{1}{2}$, find the value of $\cos X \cos Z + \sin X \sin Z$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile