Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
Prove that:
$\cos20^\circ\cos40^\circ\cos80^\circ=\frac{1}{8}$
✓

Answer

$\text{LHS}=\cos20^\circ\cos40^\circ\cos80^\circ$
$=\ \frac{1}{2}(2\cos20^\circ\cos40^\circ)\cos80^\circ$
$=\ \frac{1}{2}[\cos(40^\circ+20^\circ)+\cos(40^\circ-20^\circ)]\cos80^\circ$$[\because\ 2\cos\text{A}\cos\text{B}=\cos(\text{A+B})+\cos(\text{A}-\text{B})]$
$=\ \frac{1}{2}[\cos60^\circ+\cos20^\circ]\cos80^\circ$
$=\ \frac{1}{2}\Big[\frac{1}{2}+\cos20^\circ\Big]\cos80^\circ$
$=\ \frac{1}{2}[\cos80^\circ+2\cos20^\circ\cos80^\circ]$
$=\ \frac{1}{4}[\cos80^\circ+\cos(80^\circ+20^\circ)+\cos(20^\circ-80^\circ)]$
$=\ \frac{1}{4}[\cos80^\circ+\cos100^\circ+\cos60^\circ]$
$=\ \frac{1}{4}[\cos80^\circ+\cos(180^\circ-80^\circ)+\cos60^\circ]$
$=\ \frac{1}{4}[\cos80^\circ-\cos80^\circ+\cos60^\circ]$
$= \frac{1}{4}\Big[\frac{1}{2}\Big]=\frac{1}{8}=\text{RHS}$

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 "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Sketch the graphs of the following functions:
$\text{f(x)}=\text{cosec}^2\text{x}$
→
Solve the following equations:
$\cot\text{x}+\tan\text{x}=2$
→
Prove that:
$\frac{\sin\text{A}+2\sin3\text{A}+\sin5\text{A}}{\sin3\text{A}+2\sin5\text{A}+\sin7\text{A}}=\frac{\sin3\text{A}}{\sin5\text{A}}$
→
Two ships leave a port at the same time. One goes 24km/ hr in the direction N 38° E and other travels 32km/ hr in the direction S 52° E. Find the distance between the ships at the end of 3hrs.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^3+3\text{x}^2+6\text{x}+2}{\text{x}^3+3\text{x}^2-3\text{x}-1}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sqrt{2\sin\text{x}}-1}{\big(\frac{\pi}{2}-\text{x}\big)}$
→
Show that for any sets A and B,

$\text{A}\cup(\text{B}-\text{A})=(\text{A}\cup\text{B})$

→
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66km/ hr. Through what angle has it turned in 10 seconds?
→
Represent to solution set of each of the following inequations graphically in two dimensional plane:
$0\leq2\text{x}-5\text{y}+10$
→
The equation of the line through the intersection of the the lines 2x - 3y = 0 and 4x - 5y = 2 and
column I column II
(a) Throught the point (2, 1) is (a) 2x - y = 4
(b) perpendicular to the line x + 2y + 1 = 0 is (b) x + y - 5 = 0
(c) parpallel to the line 3x + 4y + 5 = 0 (c) x - y - 1
(d) Equally inlined to the axis is (d) 3x - 4y - 1 = 0
→