Q. 93.6( 62 Votes )

# Prove that

Answer :

We have, y =    Now,  8cosθ + 4 = 4 + cos2θ + 4cosθ

cos2θ - 4cosθ = 0

cosθ(cosθ-4) = 0

cosθ = 0 or cosθ = 4

Since, cosθ≠4, cosθ = 0

cosθ = 0 θ = π/2

Now,   In interval, , we have cos θ > 0. Also, 4 > cos θ

4 – cosθ > 0

Therefore, cosθ(4 cosθ) > 0 and also (2 + cosθ)2 > 0  Therefore, y is strictly increasing in interval .

Also, the given function is continuous at x = 0 and x = .

Therefore, y is increasing in interval .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Show that the altMathematics - Board Papers

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1