Answer
Verified
479.1k+ views
Hint: In this question we have to find the number of solutions of the given equation. To solve this question the main point is that the value of $\cos x$ is less than or equal to 1. At $x=0$ the value of cos is always to be 1.
Complete step-by-step answer:
In this question we have been given the equation $\cos \left( {\pi \sqrt {x - 4} } \right) \cdot \cos \left( {\pi \sqrt x } \right) = 1$
The RHS is 1 and both terms in multiplication in LHS are in cosine.
Now both terms can only be less than or equal to 1. But if anything less than 1 is multiplied with something less than 1, then we can never get 1 in RHS.
So, $\cos \left( {\pi \sqrt {x - 4} } \right) = 1$ and $\cos \left( {\pi \sqrt x } \right) = 1$
$ \Rightarrow \sqrt {x - 4} = 0$ and $\sqrt x = 0$
$ \Rightarrow x = 4{\text{ and }}x = 0$
As x=4 is only given in the options
And hence, option A is correct.
Note: Whenever we face such types of problems the key point to remember is that we need to have a good grasp over trigonometric properties, some of which have been used above. We must remember that the maximum value of sine and cosine is 1. This helps in getting us the required condition and gets us on the right track to reach the answer.
Complete step-by-step answer:
In this question we have been given the equation $\cos \left( {\pi \sqrt {x - 4} } \right) \cdot \cos \left( {\pi \sqrt x } \right) = 1$
The RHS is 1 and both terms in multiplication in LHS are in cosine.
Now both terms can only be less than or equal to 1. But if anything less than 1 is multiplied with something less than 1, then we can never get 1 in RHS.
So, $\cos \left( {\pi \sqrt {x - 4} } \right) = 1$ and $\cos \left( {\pi \sqrt x } \right) = 1$
$ \Rightarrow \sqrt {x - 4} = 0$ and $\sqrt x = 0$
$ \Rightarrow x = 4{\text{ and }}x = 0$
As x=4 is only given in the options
And hence, option A is correct.
Note: Whenever we face such types of problems the key point to remember is that we need to have a good grasp over trigonometric properties, some of which have been used above. We must remember that the maximum value of sine and cosine is 1. This helps in getting us the required condition and gets us on the right track to reach the answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE