Question : If $\cos x+\sin x=\sqrt{2} \cos x$, what is the value of $(\cos x-\sin x)^2+(\cos x+\sin x)^2$?
Option 1: $2$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{1}{\sqrt{2}}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $2$
Solution : Given: $\cos x+\sin x=\sqrt{2} \cos x$ To find, $(\cos x-\sin x)^2+(\cos x+\sin x)^2$ $=\cos^2 x + \sin^2 x - 2\sin x \cos x + \cos^2 x + \sin^2 x + 2\sin x \cos x $ $=1 - 2 \sin x \cos x + 1 + 2\sin x \cos x = 1 + 1 = 2$ Hence, the correct answer is $2$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : In $\triangle{XYZ}$, right-angled at $Y$, if $\sin X = \frac{1}{2}$, find the value of $\cos X \cos Z + \sin X \sin Z$.
Question : If $\tan \frac{A}{2}=x$, then find $x$.
Question : Using $\cos (A+B)=\cos A \cos B-\sin A \sin B$, find the value of $\cos 75^\circ$.
Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.
Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile