Prove that: ^2 2x- ^2 6x = 4x 8x - Vidyadip

Question

Prove that: $\cos^2 2x-\cos^2 6x = \sin 4x \sin 8x$

✓

Answer

We have L.H.S$= \cos^2 2x-\cos^2 6x$
[$\because \cos^2B - \cos^2A = \sin (A+B) \sin (A - B)] $
$= \sin 8 x \sin 4x =$ R.H.S.

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 Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\left(\frac{8 k+2}{k+1}, \frac{-3}{k+1}, \frac{10 k+4}{k+1}\right)$].

Prove that: $ \cos 4x = 1 - 8 \sin^2x \cos^2x$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-1}{\sqrt{1-\cos\text{x}}}$

Show the of the following progression is G.P. Also, find the common ratio in case:$4,-2,1,\frac{-1}{2}.\dots$

The runs scored by players in $10$ matches are $38, 70, 48, 34, 42, 55, 63, 46, 54, 44.$ Find the variance and standard deviation.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cap$ B)' = A' $\cup$ B'.

In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics?

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum:$ x^2 = -16y$

Redefine the function $\text{f(x)}=|\text{x}-2|+|2+\text{x}|, -3\leq\text{x}\leq3.$

Differentiate the following functions with respect to x:$\frac{\text{e}^\text{x}+\sin\text{x}}{1+\log\text{x}}$