Question

If Sec A-tanA=4 then cosec A

Answer 1

Sec A-tanA=4 -------- (1)

sec^2A - tan^2A = 1

(Seca-tana)(Seca+tana) = 1

(4)(Seca+tana) = 1

Seca+tana = 1/4 ---------- (2)

On Adding (1) & (2

Seca - tana + Seca + tana = 4 + 1/4

2seca = 17/4

Seca = 17/8  ---------- (3)

On subtracting (1) & (2), we get

Seca+tana - (seca - tana) = 4 - 1/4

Seca + tana - seca + tana = 15/4 

2tana = 15/4

tana = 15/8   ---------- (4)

We know that cosec theta = sec theta/tan theta

Therefore, cosec a =17/8/15/8=17/15

Hope its correct<3

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