Question : The value of $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\tan ^2 60^{\circ}-\sin ^2 30^{\circ}-\cos ^2 45^{\circ}}$ is:
Option 1: $\frac{67}{27}$
Option 2: $\frac{22}{9}$
Option 3: $\frac{67}{24}$
Option 4: $\frac{19}{9}$
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: $\frac{67}{27}$
Solution : Given expression, $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\tan ^2 60^{\circ}-\sin ^2 30^{\circ}-\cos ^2 45^{\circ}}$ We know, $\cos 60^{\circ}=\frac12$, $\sec30^{\circ}=\frac2{\sqrt3}$, $\tan 45^{\circ}=1$, $\tan60^{\circ}=\sqrt3$, $\sin30^{\circ}=\frac12$, and $\cos45^{\circ}=\frac1{\sqrt2}$ $\frac{5\times(\frac12)^2+4(\frac2{\sqrt3})^2-1}{(\sqrt3)^2-(\frac12)^2-(\frac1{\sqrt2})^2}$ = $\frac{\frac54+\frac{16}{3}-1}{3-\frac14-\frac12}$ = $\frac{\frac{15+64-12}{12}}{\frac{12-1-2}{4}}$ = $\frac{67}{9\times3}$ = $\frac{67}{27}$ Hence, the correct answer is $\frac{67}{27}$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : The value of $\frac{4 \tan ^2 30^{\circ}+\sin ^2 30^{\circ} \cos ^2 45^{\circ}+\sec ^2 48^{\circ}-\cot ^2 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ}+\sin 37^{\circ} \cos 53^{\circ}+\tan 18^{\circ} \tan 72^{\circ}}$ is:
Question : The value of $\cos^{2}30^{\circ}+\sin^{2}60^{\circ}+\tan^{2}45^{\circ}+\sec^{2}60^{\circ}+\cos0^{\circ}$ is:
Question : If $x\sin ^{2}60^{\circ}-\frac{3}{2}\sec 60^{\circ}\tan^{2}30^{\circ}+\frac{4}{5}\sin ^{2}45^{\circ}\tan ^{2}60^{\circ}=0$, then $x$ is:
Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Question : The value of $\frac{2 \tan 60^{\circ}}{1+\tan ^2 60^{\circ}}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile