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greatest value of 1/sin^6 x + cos^6 x

greatest value of 1/sin^6 x + cos^6 x

Grade:11

3 Answers

Lab Bhattacharjee
121 Points
8 years ago
\text{HINT: }\\ (\sin^2x)^3+(\cos^2x)^3\\ =(\sin^2x+\cos^2x)^3-3(\sin^2x\cos^2x)(\sin^2x+\cos^2x)\\ =1-\dfrac34\sin^22x=1-\dfrac38(1-\cos4x)
Lab Bhattacharjee
121 Points
8 years ago
\text{HINT:}\\ (\sin^2x)^3+(\cos^2x)^3=\dfrac{(1-\cos2x)^3+(1+\cos2x)^3}8\\ =\dfrac{2+3\cdot2\cos^22x}4\\ =\dfrac{2+3(1+\cos4x)}4
Raghu Vamshi Hemadri
72 Points
8 years ago
Its infinity as for some X Sin^6X can be 0.
 

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