1.

Find the Minimum value of 9 cos 2x + 2 sec 2x1). 3√22). 2√33). 6√34). 6√2

Answer»

Solution:

According to AM-GM inequality,

(a + B)/2 ≥ √ab 

Here a = 9 cos²x and b = 2 sec²x

Note: AM- GM inequality can be used ANYWHERE keeping in mind that a and b are positive.

So, (9 cos²x + 2 sec²x)/2≥√(9cos²x)(2sec²x)

(9 cos²x + 2 sec²x)/2≥√(9/sec²x)(2sec²x)

(9 cos²x + 2 sec²x)/2≥√(9)(2)

(9 cos²x + 2 sec²x)/2≥√18

(9 cos²x + 2 sec²x)≥2√18

(9 cos²x + 2 sec²x)≥2×3√2

(9 cos²x + 2 sec²x)≥6√2

So, the minimum value is 6√2.

The correct OPTION is 4). 6√2



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