Question

minimum value of( 8sec2theta+ 2cos2theta) is equal to ​

Answer 1

Answer:

The minimum value will be 8.

Step-by-step explanation:

8sec²@+2cos²@

=2[(2sec@)²+(cos@)²]

=2[(2sec@-cos@)²+2×2sec@×cos@]

=2(2sec@-cos@)² +2×2×2

[as sec@× cos@=1]

=(2sec@-cos@)²+8

Now if (2sec@-cos@)² become 0 then we can say it's minimum value will be 8.

Note value of (2sec@-cos@)² can't be negative because no square of real number is negative.

So it's minimum value will be 8.

We can determine the answer using derivation process also.

Assume f(@)=8sec²@+2cos²@

The determine the value of f'(@) and equate with 0.

Put the value cos²@=2 in f''(@) .

Thus you can determine the answer also. But at first ensure that you know what is derivation process. Otherwise use the first process.

PLEASE MARK AS BRAINLIEST ANSWER DON'T FORGET TO PRESS ON THANKS IF YOU FIND IT HELPFUL