If sec theta - tan theta=4 ,then find the value of cosec theta
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Answered by
71
Given SecФ - Tan Ф = 4 ----(1)
Multiply both sides by SecФ + TanФ to get:
Sec²Ф - Tan²Ф = 4 (SecФ + TanФ)
=> SecФ + TanФ = 1/4 ---- (2)
From (1) & (2), SecФ = 17/8 and Tan Ф = -15/8
So SinФ = - 15/17
=> CosecФ = - 17/15 negative real number.
Multiply both sides by SecФ + TanФ to get:
Sec²Ф - Tan²Ф = 4 (SecФ + TanФ)
=> SecФ + TanФ = 1/4 ---- (2)
From (1) & (2), SecФ = 17/8 and Tan Ф = -15/8
So SinФ = - 15/17
=> CosecФ = - 17/15 negative real number.
kvnmurty:
:-)
How did u get sin theta from sec theta and tan theta?
Sine = tan/ sec = tan × cos
Ok.Now I got it.Thnx bro
Hey, he is sir not bro so please call him sir ( he is senior of brainly "Kvnmurty sir" )
Oh sorry. I didn't knew it.
Thnx sir.I meant no,offence.
Answered by
44
Sec theta -tan theta=4......1 equation
Multiply both side by (sec theta+tan theta)
We get,sec²theta-tan²theta=4 (sec theta +tan theta)
We get,1=4(sec theta+tan theta)
(Sec theta+tan theta)=1/4.......(2)
equation
From equation (1)and (2) we add
We get,
Sec theta -tan theta=4
Sec theta+tan theta)=1/4
We get, sec theta= 4+1/4
Sec theta=17/8 ,cos theta=8/17
And tan theta=1/4-17/8= -15/8
Then tan theta=sin theta /cos theta
Sin theta=tan theta×cos theta
Sin theta= -15/8 × 8/17 here 8 is cancelled
Sin theta = -15/17 =>cosec theta= -17/15
Multiply both side by (sec theta+tan theta)
We get,sec²theta-tan²theta=4 (sec theta +tan theta)
We get,1=4(sec theta+tan theta)
(Sec theta+tan theta)=1/4.......(2)
equation
From equation (1)and (2) we add
We get,
Sec theta -tan theta=4
Sec theta+tan theta)=1/4
We get, sec theta= 4+1/4
Sec theta=17/8 ,cos theta=8/17
And tan theta=1/4-17/8= -15/8
Then tan theta=sin theta /cos theta
Sin theta=tan theta×cos theta
Sin theta= -15/8 × 8/17 here 8 is cancelled
Sin theta = -15/17 =>cosec theta= -17/15
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