Question

find the minimum value of cos^4theta +sin^2theta​

Answer 1

Answer:Sin^2 (x) + cos^4(x)

Cos^4(x) +1-cos^2(x)

Cos^2(x){cos^2(x)-1}+1

1-sin^2(x)cos^2(x)…….eq(1)

Now we know that sin2x=2sin(x)cos(x)

Sin(x)cos(x)=sin(2x)/2

Now we have square both side we get

Sin^2(x)cos^2(x)=sin^2 (2x)/4

Now putting this value in eq 1 we get

1-sin^2(2x)/4….eq 2

Now to get eq2 min value the -ve part should be max(I.e) sin function must have max value (I.e 1)

Now 1-1/4=3/4 is min value

Now to get

Step-by-step explanation: