Prove that `(sintheta+cosectheta)^2+(costheta+sectheta)^2ge9`. – InterviewSolution

InterviewSolution

1.	Prove that `(sintheta+cosectheta)^2+(costheta+sectheta)^2ge9`.
Answer» `(sintheta+cosectheta)^2+(costheta+sectheta)^2` `=sin^2theta+cosec^2 theta+2+cos^2theta+sec^2theta+2` `=(sin^2theta+cos^2theta)+(cosec^2theta+sec^2theta)+4` `=5+1+tan^2thetta+1+cot^2theta` `=7+(tantheta-cottheta)^2+2` `=9+(tantheta-cottheta)^2ge9`

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