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If A = sin^2 theta+ cos^4 theta, then f...

If `A = sin^2 theta+ cos^4 theta`, then for all real values of `theta`

A

`1leAle2`

B

`(3)/(4) le A le 1`

C

`(13)/(16) le A le 1`

D

`(3)/(4) le A le (13)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `A - sin^(2) theta+(1-sin^(2) theta)^(2)`
`implies A = sin^(4) theta - sin^(2) theta + 1`
`implies A = (sin^(2)theta-(1)/(2))^(2)+(3)/(4)`
`implies 0le (sin^(2)theta-(1)/(2))^(2)le(1)/(4) " "[because 0 le sin^(2) theta le 1]`
`therefore (3)/(4) le A le 1`
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