Download App

Trigonometric Ratios Of Compound Angles — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compound Angles1 Mark
Question
Write the value of $\cos\frac{\pi}{7}\cos\frac{2\pi}{7}\cos\frac{4\pi}{7}.$
✓

Answer

$\cos\frac{\pi}{7}.\cos\frac{2\pi}{7}.\cos\frac{4\pi}{7}$
$=\frac{2.\sin\frac{pi}{7}.\cos\frac{\pi}{7}.\cos\frac{2\pi}{7}.\cos\frac{4\pi}{7}}{2\sin\frac{\pi}{7}}$ $\big[$Divide and multiply by $2\sin\frac{\pi}{7}\big]$
$=\frac{2.\sin\frac{2\pi}{7}.\cos\frac{\pi}{7}.\cos\frac{2\pi}{7}.\cos\frac{4\pi}{7}}{2.2\sin\frac{\pi}{7}}$
$=\frac{2\sin\frac{4\pi}{7}.\cos\frac{4\pi}{7}}{2.4\sin\frac{\pi}{7}}$
$=\frac{\sin\frac{8\pi}{7}}{8\sin\frac{\pi}{7}}$
$=\frac{\sin\big(\pi+\frac{\pi}{7}\big)}{8\sin\frac{\pi}{7}}$
$=\frac{-1}{8}$

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 "1 Marks Question" from Trigonometric Ratios Of Compound Angles→Trigonometric Ratios Of Compound Angles — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

There are 200 individual with a skin disorder, 120 has been exposed to chemical C1, 50 to chemical C2 and 30 to both the chemicals C1 and C2. Find the number of individual exposed to chemical C1 or chemical C2
→
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $B \cap D$
→
Find the slope of the line passing through the points (3, -2) and (-1, 4).
→
From the sets given below, pair the equivalent sets:
A = {1, 2, 3},
B = {t, p, q, r, s},
C = $\{\alpha,\beta,\gamma\},$
D = {a, e, i, o, u}.
→
If cot x  $= -\frac{5}{12}$, x lies in second quadrant, find the values of other five trigonometric functions.
 
→
Write the negation of the following simple statement:
The number 17 is prime.
→
If P = {a, b, c} and Q = {r}, form the sets P $\times$ Q and Q $\times$ P. Are these two products equal?
→
What is the difference between a collection and a set? Give reasons to support your answer?
→
Compute: $\frac{12 !}{(10 !)(2 !)}$
→
Let A = {1, 2, {3, 4 }, 5}. Is the statement {$\phi$} $\subset$ A incorrect and why?
→