( 4 +x )+ ( 4 -x )=2 x - Vidyadip

Question

$\cos \left(\frac{\pi}{4}+x\right)+\cos \left(\frac{\pi}{4}-x\right)=\sqrt{2} \cos x$

✓

Answer

L.H.S.
$\begin{aligned}
& =\cos \left(\frac{\pi}{4}+x\right)+\cos \left(\frac{\pi}{4}-x\right) \\
& =2 \cos \left(\frac{\frac{\pi}{4}+x+\frac{\pi}{4}-x}{2}\right) \cos \left(\frac{\frac{\pi}{4}+x-\left(\frac{\pi}{4}-x\right)}{2}\right) \\
& =2 \cos \frac{\pi}{4} \cos x \\
& =2\left(\frac{1}{\sqrt{2}}\right) \cos x \\
& =\sqrt{2} \cos x \\
& =\text { R.H.S. }
\end{aligned}$

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 Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.

Find the modulus and amplitude for each of the following complex numbers: √3 + √2 i

How many teterms are there in the A.P. $-1,-\frac{5}{6},-\frac{2}{3},-\frac{1}{2},\ ...,\frac{10}{3}?$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin3\text{x}}{5\text{x}}$

Find the equation of the parabola whose vertex is O(0, 0) and focus at (-7, 0).

In a single toss of a fair die, what are the odds against the event that number 3 or 4 turns up?

Evaluate the following limits:
$\lim _{u \rightarrow 1}\left[\frac{u^4-1}{u^3-1}\right]$

Express the recurring decimal 0.125125125 ... as a rational number.

Find the equation of the tangent to the circle
$
x^2+y^2-4 x-6 y-12=0 \text { at }(-1,-1)
$

If the nth term of the A.P. $9, 7, 5, ...$ is same as the $n^{th}$ term of the A.P. $15, 12, 9, ...$ find $n$.