Question

[
begin{aligned}
A &=cos ^{2} theta+sin ^{4} theta
Rightarrow A=& sin ^{4} theta+1-sin ^{2} theta
&=sin ^{4} theta-sin ^{2} theta+1
end{aligned}
]
( Rightarrow A=left(sin ^{2} theta-frac{1}{2}right)^{2}+frac{operatorname{sen} 3}{4} )
- A man when, ( sin ^{2} theta frac{1}{2}=0 )
[
Rightarrow A_{min }=frac{3}{4}
]
Amax, when ( sin ^{2} theta-frac{1}{2} ) is max,
[
begin{aligned}
& 0 leq sin ^{2} theta leq 1
Rightarrow quad-frac{1}{2} & leq sin ^{2} 0-frac{1}{2} leq 1 / 2
therefore quad A max &=left(frac{1}{2}right)^{2}+frac{3}{4}=7
end{aligned}
]
[
therefore quad frac{3}{4} leq A leq 1
]
(B) Ans

# Q.2 If A = cos20 + sin40, then for all value of [AIEEE-2011] (A) 1 SAS 2 (B) Asi Q.8 If cosec (C) Asi (D) None of these 0.3 In a APQR if 3 sin P + 4 cos 0 = 6 and

Solution