Question : What is the value of $5\sin^260^{\circ}+7\sin^245^{\circ}+ 8\cos^245^{\circ}$?
Option 1: 10
Option 2: $\frac{57}{4}$
Option 3: 25
Option 4: $\frac{45}{4}$
Correct Answer: $\frac{45}{4}$
Solution :
Given: The expression is $5\sin^260^{\circ}+7\sin^245^{\circ}+ 8\cos^245^{\circ}$.
We know that trigonometric values of $\sin60^{\circ}=\frac{\sqrt3}{2}$, $\sin45^{\circ}=(\frac{1}{\sqrt2})$, and $\cos45^{\circ}=(\frac{1}{\sqrt2})$.
$5\sin^260^{\circ}+7\sin^245^{\circ}+ 8\cos^245^{\circ}$
$=5\times(\frac{\sqrt3}{2})^2+7\times(\frac{1}{\sqrt2})^2+ 8\times(\frac{1}{\sqrt2})^2$
$=5\times\frac{3}{4}+7\times\frac{1}{2}+ 8\times\frac{1}{2}$
$=\frac{15}{4}+\frac{7}{2}+4$
$=\frac{15+14+16}{4}=\frac{45}{4}$
Hence, the correct answer is $\frac{45}{4}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
