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 "(Each question 1 marks)" from Trigonometric Ratios Of Compounds→Trigonometric Ratios Of Compounds — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the maximum and minimum values of $3\cos\text{x}+4\sin\text{x}+5.$

Write the equation of the hyperbola whose vertices are $(\pm3,0)$ and foci at $(\pm5,0).$

In any $\triangle\text{ABC},$ find the value of $\sum\text{a}(\sin\text{B}-\sin\text{C})$

Find out the following sentences are statements and which are not. Justify your answer. Every set is a finite set.

Write down the all possible proper subset of the given set. {1, 2}

If the parabola $y^2 = 4ax$ passes through the point (3, 2), then find the length of its latusrectum.

The given set is the example of an empty set or not?
{x : x is a point common to any two parallel lines}.

How many words with or without, meaning can be formed using all the letters of the word EQUATION, using each letter exactly once?

Let A = {1, 2} and B = {3, 4}. Write $A \times B$. How many sub sets will $A \times B$ have? List them.

Write down the all possible subset of the given set.
{0, 1}