Prove that: 80^ + 40^ - 20^ =0 - Vidyadip

Question

Prove that:
$\cos80^\circ+\cos40^\circ-\cos20^\circ=0$

✓

Answer

$\text{LHS}=\cos80^\circ+\cos40^\circ-\cos20^\circ$
$(\cos80^\circ+\cos40^\circ)-\cos20^\circ$
$=\ 2\cos\Big(\frac{80^\circ+40^\circ}{2}\Big)\cos\Big(\frac{80^\circ-40^\circ}{2}\Big)-\cos20^\circ$ $\Big[\because\ \sin\text{c}-\sin\text{D}=2\sin\Big(\frac{\text{C}-\text{D}}{2}\Big)\cos\Big(\frac{\text{C+D}}{2}\Big)\Big]$
$=\ 2\cos60^\circ\cos20^\circ-\cos20^\circ$
$=\ 2\times\frac{1}{2}\cos20-\cos20^\circ$
$=\ \cos20^\circ-\cos20^\circ$
$=\ 0$
$=\ \text{RHS}$

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 "2 Marks Questions" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If A and B are two events associated with a random experiment such that P(A) = 0.5, P(B) = 0.3 and $\text{P}(\text{A}\cap\text{B})=0.2,$ find $\text{P}(\text{A}\cup\text{B}).$

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$-1,\frac{1}{4},\frac{3}{2},\frac{11}{4},...$

Show that if $\text{x}^2 + \text{y}^2 = 1,$ then the point $\Big(\text{x, y},\sqrt{1-\text{x}^2-\text{y}^2}\Big)$ is at a distance 1 unit from the origin.

Prove that: $\begin{equation} \frac{\sin (x+y)}{\sin (x-y)}=\frac{\tan x+\tan y}{\tan x-\tan y} \end{equation}$

For some constants a and b, find the derivative of (x - a)(x - b)

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas $y^2-4 y+4 x=0$

Prove that:
$\cos24^\circ\cos55^\circ+\cos125^\circ+\cos204^\circ+\cos300^\circ=\frac12$

Does the expansion of $\Big(2\text{x}^2-\frac{1}{\text{x}}\Big)^{20}$ contain any term involving x⁹?

Find the derivative of x² - 2 at x = 10

Find the equation of a line passing through point of intersection of lines $2 x+y=5$ and $x-2 y=$ 0 which makes an angle $45^{\circ}$ with $x$-axis.