If 4x=1+K ^2x ^2, then write the value of k. - Vidyadip

Question

If $\cos4\text{x}=1+\text{K}\sin^2\text{x}\cos^2\text{},$ then write the value of k.

✓

Answer

We have,
$\cos4\text{x}=1+\text{k}\sin^2\text{x}\cos^2\text{x}\ .....(\text{i})$
$\Rightarrow\cos2.2\text{x}-\cos^22\text{x}-\sin^2\text{x}$
$=1-2\sin^22\text{x}$
$=1-2(2\sin\text{x}\cos\text{x})^2$
$=1-8\sin^2\text{x}\cos^2\text{x}\ .....(\text{ii})$
compaiing (i) & (ii), we get
$\text{k}=-8$

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 "1 Marks Question" from Trigonometric Ratios Of Compound Angles→Trigonometric Ratios Of Compound Angles — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Write the value of $\theta\in\Big(0,\frac{\pi}{2}\Big)$ for which area of the triangle formed by points $\text{O}(0,0),\text{A} (\text{a} \cos \theta, \text{b} \sin \theta)$ and $\text{B} (\text{a} \cos \theta, − \text{b} \sin \theta)$ is maximum.

Write the lenght of the latus-rectum of the hyperbola $16\text{x}^{2}-9\text{y}^{2}=144$

Find the limit $\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + x} - 1}}{x}.$

Write the set in roster form: F = The set of all letters in the word BETTER.

Is the set $\{x : x \in N$ and $x^2 = 4\}$ finite or infinite?

If $\alpha+\beta-\gamma=\pi,$ and $\sin^2\alpha+\sin^2\beta-\sin^2\gamma=\lambda\sin\alpha\sin\beta\cos\gamma,$ then write the value of $\lambda.$

Write the conjugate of $\frac{2-\text{i}}{(1-2\text{i})^2}.$

{2, 6, 10} and {3, 7, 11} are disjoint sets.

The longest side of a triangle is three times the shortest side and third side is 2cm shorter than the longest side if the perimeter of the triangles at least 61cm, find the minimum length of the shortest-side.

Determine the contrapositive of the following statements:
If he has courage he will win.