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[" 1) Far any of "((pi)/(4)+(pi)/(2))],[...

[" 1) Far any of "((pi)/(4)+(pi)/(2))],[qquad 3(sin theta-cos theta)^(4)+6sin theta+cos theta)^(2)+4sin^(6)theta]

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For any theta epsilon((pi)/4,(pi)/2) the expression 3(sin theta-cos theta)^(4)+6(sin theta+cos theta)^(2)+4sin^(6)theta equals:

For any theta epsilon((pi)/4,(pi)/2) the expression 3(sin theta-cos theta)^(4)+6(sin theta+cos theta)^(2)+4sin^(6)theta equals:

Prove that: 3(sin theta-cos theta)^(4)+6(sin theta+cos theta)^(2)+4(sin^(6)theta+cos^(6)theta)-13=0

(cos6 theta-cos4 theta)/(sin6 theta+sin4 theta)=-tan theta

cos^(3)2 theta+3cos2 theta=4(cos^(6)theta-sin^(6)theta)

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta) is equal to

int(2sin2 theta-cos theta)/(6-cos^(2)theta-4sin theta)d theta

int_(pi//4) ^(pi//2) (cos theta)/((cos (theta/2) + sin (theta/2))^(3))d theta=

1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin theta).