Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

What is cosx times cos2x?

Answer
VerifiedVerified
453.9k+ views
like imagedislike image
Hint: Here we will first find the value of the function cos2x in terms of cosx. For doing this we will use the trigonometric identity cos(a+b)=cosacosbsinasinb where we will substitute a = b = x. Further we will use the identity cos2x+sin2x=1 to replace the sine function. Once the value of cos2xis found we will take its product with cosx to get the answer.

Complete step by step answer:
Here we have been asked to simplify the expression given by the sentence cosx times cos2x. That means we need to take the product of the cosine functions cosx and cos2x. Let us assume its mathematical expression as E, so we have,
E=cosx×cos2x
Now, first we will find the value of cos2x in terms of cosx and then we will consider the required product. So we can write the argument of cos2x as:
cos2x=cos(x+x)
Using the trigonometric identity cos(a+b)=cosacosbsinasinb and substituting a = b = x we get,
cos2x=cosx×cosxsinx×sinxcos2x=cos2xsin2x
Further simplifying the above relation by using the formula cos2x+sin2x=1 to replace the sine function we get,
cos2x=cos2x(1cos2x)cos2x=cos2x1+cos2xcos2x=2cos2x1
Substituting the above value in expression E we get,
E=cosx×(2cos2x1)E=2cos3xcosx
Hence the above relation is our answer.

Note: You can also get the answer in a different format. What you can do is write the product cosx×cos2x as 12(2cosx×cos2x) and then use the use the identity 2cosacosb=cos(a+b)+cos(ab) by considering a = 2x and b = x. In this case you will get the answer 12(cos3x+cosx) and it will also be the correct answer only the form will be different. You must remember all the trigonometric identities as they are used in other chapters and subjects also.
Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
EnglishEnglish
MathsMaths
ScienceScience
₹49,800 (9% Off)
₹45,300 per year
Select and buy