Math, asked by tejdeep46, 11 months ago

The minimum value of f(x)=cosec square x+25sec square x=
a) 26
b) 36
c) 24
d) 1

Answers

Answered by lalithadeviv3863
0

26 is the answer I think

Answered by parijindal47
1

Answer:

Let f(x) = cosec²x + 25sec²x

we know,

sec²x - tan²x = 1 , sec²x = 1 + tan²x

cosec²x - cot²x = 1 , cosec²x = 1 + cot²x

then, f(x) = 1 + cot²x + 25(1 + tan²x)

= 1 + cot²x + 25 + 25tan²x

f(x) = 26 + cot²x + 25tan²x

we know, if a and b are two positive terms,

then, AM ≥ GM

here cot²x and 25tan²x are two positive terms,

so, (cot²x + 25tan²x)/2 ≥ √{25tan²x.cot²x}

cot²x + 25tan²x ≥ 2 × √{25 × 1} = 2×5 = 10

cot²x + 25tan²x ≥ 10

add 26 both sides,

cot²x + 25tan²x + 26 ≥ 10 + 26 = 36

f(x) = cot²x + 25tan²x + 26 ≥ 36

hence, minimum value of f(x) is 36 .

hence, minimum value of cosec²x + 25sec²x = 36

hope it help you

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