Question

If sec theta - tan theta = 4 find cosec theta

Answer 1

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Answer 2

sec Ф-tanФ=4
we know that, sec^2 Ф-tan^2Ф= 1
                       (secФ-tanФ)(secФ+tanФ)=1     (∵a^2 - b^2 = (a+b)(a-b))
                       secФ - tanФ = 1/secФ+tanФ
since,
sec Ф-tanФ=4      ............i
∴sec Ф + tanФ=1/4..............ii
Add equation i and ii
2secФ = 4 +1/4
           = 17/4
secФ = 17/8
tanФ =  -15/8

1/cosФ - sinФ/cosФ = 4
17/8(1-sinФ) = 4
1-sinФ = 4*8/17
sinФ = 1-32/17
        = 17-32/17
        =  -15/17      
∴cosecФ = 1/sinФ = -17/15


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