Answer :

Given: (cosec θ – sin θ) = a3

(sec θ – cos θ) = b3


Since, a3 = (cosec θ – sin θ)


= (1/sin θ) – sin θ


=


= cos2 θ/sin θ


Therefore, a2 = (a3)2/3 = (cos2 θ/sin θ)2/3


Also, b3 = sec θ – cos θ


= (1/cos θ) – cos θ


= (1 – cos2 θ)/cos θ


= sin2 θ/cos θ


Therefore, b2 = (b3)2/3 = (sin2 θ/cos θ)2/3


Now, consider the left – hand side:


a2 b2 (a2 + b2) =


=


=


= sin2 θ + cos2 θ


= 1 = R.H.S.


Hence, proved.


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
caricature
view all courses
RELATED QUESTIONS :

Prove the followiKC Sinha - Mathematics

Prove the followiKC Sinha - Mathematics

Prove the followiKC Sinha - Mathematics

If sin 77° = x, tKC Sinha - Mathematics

If cos55° = x<supKC Sinha - Mathematics

If cos40o</sKC Sinha - Mathematics