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

Prove the following trigonometric equation
cos24+cos55+cos125+cos204+cos300=12

Answer
VerifiedVerified
509.4k+ views
like imagedislike image
Hint: - Break the angles as a sum of other angles with multiples of 90.
Taking the L.H.S.
cos24+cos55+cos125+cos204+cos300 --- (1)
As we know that
[cos(180θ)=cosθcos(180+θ)=cosθcos(360θ)=cosθ]
So we have:
cos125=cos(18055)=cos55cos204=cos(180+24)=cos24cos300=cos(36060)=cos60
Putting these values in equation (1) we get,
cos24+cos55cos55cos24+cos60cos6012=R.H.S.
Hence the equation is proved.

Note - The following problem can also be solved by putting in the values of each of the terms, but it is easier to solve the problem by breaking the angles as a sum of other angles with multiple of 90. Also some of the common trigonometric identities must be remembered.