The least value of 6tan2ϕ +54cot2ϕ is (I) 54 when A.M≥G.M is applicable for 6tan2ϕ ,54cot2ϕ ,18(II) 54 when A.M≥G.M is applicable for 6tan2ϕ ,54cot2ϕ ,18 is added further(III) 78 when tan2ϕ =cot2ϕ

by applying A.M≥G.M in 6tan2ϕ +54cot2ϕ +18 we get36tan2ϕ +54cot2ϕ +18≥(6×54×18) 1/3≥18Now equality holds when6tan2ϕ =54cot2ϕ =18⇒tan2ϕ =3;cot2ϕ =31Hence, the statements I and II are correct.

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The least value of 6 ^{ 2 }{ } +54 ^{ 2 }{ } is (I) 54 wh

Question

The least value of $6 tan^{2} ϕ + 54 cot^{2} ϕ$ is
(I) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$
(II) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$ is added further
(III) $78$ when $tan^{2} ϕ = cot^{2} ϕ$

(I) is correct, (II) is false

(I) and (II) are correct

(III) are correct

none of the above are correct

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Noah Discussed

The least value of

6 tan^{2} ϕ + 54 cot^{2} ϕ

is
(I)

54

when

A . M \geq G . M

is applicable for

6 tan^{2} ϕ, 54 cot^{2} ϕ, 18

(II)

54

when

A . M \geq G . M

is applicable for

6 tan^{2} ϕ, 54 cot^{2} ϕ, 18

is added further
(III)

78

when

tan^{2} ϕ = cot^{2} ϕ

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

by applying

A . M \geq G . M

6 tan^{2} ϕ + 54 cot^{2} ϕ + 18

we get

\frac{6 tan ^{2} ϕ + 54 cot ^{2} ϕ + 18}{3} \geq (6 \times 54 \times 18)^{1/3} \geq 18

Now equality holds when

6 tan^{2} ϕ = 54 cot^{2} ϕ = 18 \Rightarrow tan^{2} ϕ = 3; cot^{2} ϕ = \frac{1}{3}

Hence, the statements I and II are correct.

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Question Text	The least value of $6 tan^{2} ϕ + 54 cot^{2} ϕ$ is (I) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$ (II) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$ is added further (III) $78$ when $tan^{2} ϕ = cot^{2} ϕ$
Answer Type	Text solution:1
Upvotes	150

The least value of 6tan2ϕ +54cot2ϕ is (I) 54 when A.M≥G.M is applicable for 6tan2ϕ ,54cot2ϕ ,18(II) 54 when A.M≥G.M is applicable for 6tan2ϕ ,54cot2ϕ ,18 is added further(III) 78 when tan2ϕ =cot2ϕ

Text solutionVerified

Practice questions from similar books

The least value of $6 tan^{2} ϕ + 54 cot^{2} ϕ$ is
(I) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$
(II) $54$ when $A . M \geq G . M$ is applicable for $6 tan^{2} ϕ, 54 cot^{2} ϕ, 18$ is added further
(III) $78$ when $tan^{2} ϕ = cot^{2} ϕ$