if sec theta -tan theta =4,then prove that cos theta=8/17
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Answered by
290
Hi !
secθ - tanθ = 4 -----> (1)
Multiplying and dividing by secθ +tanθ
= secθ - tanθ × secθ +tanθ/secθ +tanθ
= sec²θ - tan²θ/secθ + tanθ = 4
we know that --> sec²θ - tan²θ = 1
1/secθ + tanθ = 4
therefore ,
secθ + tanθ = 1/4 ----> (2)
------------------------------------------------------------------------
Adding equations (1) and (2) :-
secθ - tanθ = 4
secθ + tanθ = 1/4
---------------------------
2secθ = 4 + 1/4
2secθ = 17/4
secθ = 17/4*2
= 17/8
we know that
cosθ = 1/secθ
= 1/(17/8)
= 8/17
Proved !
secθ - tanθ = 4 -----> (1)
Multiplying and dividing by secθ +tanθ
= secθ - tanθ × secθ +tanθ/secθ +tanθ
= sec²θ - tan²θ/secθ + tanθ = 4
we know that --> sec²θ - tan²θ = 1
1/secθ + tanθ = 4
therefore ,
secθ + tanθ = 1/4 ----> (2)
------------------------------------------------------------------------
Adding equations (1) and (2) :-
secθ - tanθ = 4
secθ + tanθ = 1/4
---------------------------
2secθ = 4 + 1/4
2secθ = 17/4
secθ = 17/4*2
= 17/8
we know that
cosθ = 1/secθ
= 1/(17/8)
= 8/17
Proved !
Anonymous:
2sec theta = 4 + 1/4
oh
2 sec theta = 16/4 + 1/4
tq
sec theta = 17/4*2
thts all
tq a lot
:)
If tan squared theta+3=3 sec theta,0 less than theta less than 90.find theta
plz answer to that quetsion
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