If sec thetha + tan theta =p then tan theta is equal to
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Answer:
Given sec x + tan x = p .....(i)
We know that sec²x-tan²x=1
So (sec x + tan x)(sec x - tan x)=1
or p(sec x - tan x)=1
or sec x - tan x =(1/p) .....(ii)
Subtracting equation (i) by (ii)
we get,
tan x = (p²-1)/2p
If my answer satisfies you then give me thanks.
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Answer:
for convinience i would like to write theta as x
we know that sec x + tan x = p
now 1/p = 1/(sec x + tan x)
also 1 = sec^2 x - tan^2 x = (sec x + tan x)(sec x - tan x)
thus 1/p = (sec x + tan x)(sec x - tan x)/(sec x + tan x)
ie: 1/p = sec x - tan x
so p - 1/p = 2 tan x
=> tan x = (p - 1/p)/2
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