Prove that: 24^ 55^ + 125^ + 204^ + 300^ = 12 - Vidyadip

Question

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

✓

Answer

$\text{L.H.S}=\cos24^\circ+\cos55^\circ+\cos125^\circ+\cos204^\circ+\cos300^\circ$
$=\cos24^\circ+\cos204^\circ+\cos55^\circ+\cos125^\circ+\cos300^\circ$
$=\cos24^\circ+\cos(\pi+24^\circ)+\cos55^\circ+\cos(\pi-55^\circ)+\cos\Big(2\pi-\frac{\pi}{3}\Big)$
$=\cos24^\circ-\cos24^\circ+\cos55^\circ+\cos55^\circ-\cos\frac{\pi}{3}$
$=\cos\frac{\pi}{3}$
$=\frac{1}{2}$
$=\text{R.H.S}$
$\text{Proved}$

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 "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the y-intercept of the line whose slope is $4$ and which has x-intercept $5.$

If $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$, show that $A-4 A+3 I=0$.

Solve the following system of equations in R.
$\frac{2\text{x}+1}{7\text{x}-1}>5,\frac{\text{x}+7}{\text{x}-8}>2$

If $\tan \theta+\frac{1}{\tan \theta}=2$ then find the value of $\tan ^2 \theta+\frac{1}{\tan ^2 \theta}$

If $A=\left[\begin{array}{cc}5 & 4 \\ -2 & 3\end{array}\right]$ and $\left[\begin{array}{cc}-1 & 3 \\ 4 & -1\end{array}\right]$ then find $C^{\top}$, such that $3 A-2 B+C=I$, where $I$ is the

unit matrix of order 2.

Find the domain and range of the following functions.

$\mathrm{g}(\mathrm{x})=\frac{x+4}{x-2}$

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow0^-}(1+\text{cosec }\text{x})$

If $A=\left[\begin{array}{ccc}2 & 3 & -1 \\ 4 & 7 & 5\end{array}\right], B=\left[\begin{array}{ccc}1 & 3 & 2 \\ 4 & 6 & -1\end{array}\right]$ and
$C=\left[\begin{array}{ccc}1 & -1 & 6 \\ 0 & 2 & -5\end{array}\right]$, find the matrix $X$ such that
$
3 \mathrm{~A}-2 \mathrm{~B}+4 \mathrm{X}=5 \mathrm{C} \text {. }
$

Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.