Find the domain of sin^2x + cosec^2x
Answers
Step-by-step explanation:
What is the maximum value of sin2x+csc2x ?
Don't miss India's superhits!
Use the AM ≥ GM, inequality for sin2x and cosec2x :
sin2x+cosec2x2≥(sin2x.cosec2x)−−−−−−−−−−−−−√
⟹sin2x+cosec2x2≥1 , since (sin2x.cosec2x)=1
So what does it tell about the maximum value of sin2x+cosec2x ?
Yes absolutely, this expression doesn't have a maximum value. But yes the minimum value is 2 .
Another way to see this is by considering the function
f(x)=sin2x+cosec2x=(sinx−cosecx)2+2.sinx.cosecx=(sinx−cosecx)2+2=(sinx−1sinx)2+2=2+(−cos2xsinx)=2+cot2xcosec2x
Since, both cotx and cosecx takes infinitely large values therefore the function f(x) also takes infinitely large values, implying f has no maximum value.
Answer:
^4x mark as brainly thanks if uncorrect sorry