Question

If tan theta is equals to one by root seven then prove that cosec square theta plus sec Square theta divided by cosec square theta minus Sec square theta is equals to 4/3

Answer 1

Answer:

Given :

tan x = 1/√7

To Prove :

(cosec²x + sec²x) / (cosec²x - sec²x) = 4/3

Proof :

tanx = 1/√7

tan²x = 1/7

cot²x = 7

We know, sec²x - tan²x = 1

sec²x = 1 + tan²x

sec²x = 1 + 1/7

sec²x = 8/7

cosec²x = 1 + cot²x

cosec²x = 1 + 7

cosec²x = 8

Now, putting on the equation,

= (cosec²x + sec²x) / (cosec²x - sec²x)

= (8 + 8/7) / (8 - 8/7)

= [(56 + 8)/56]/[(56 - 8)/56]

= 64 / 48

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