Question

If secA - tanA = 4, then find cosecA.

Points: 10

Answer 1

Given Equation is Seca - tana = 4.   -------- (1)

We know that sec^2A - tan^2A = 1.

We know that (a^2 - b^2) = (a-b)(a+b).

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

(4)(Seca+tana) = 1

Seca+tana = 1/4   ---------- (2).


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

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.


On solving (3) & (4), we get

cosec a = $\frac{17}{ \frac{8}{ \frac{15}{8} } }$

              = $\frac{17}{15}$



Hope this helps!

Answer 2

ANSWER
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We know that sec^2A - tan^2A = 1.

We know that (a^2 - b^2) = (a-b)(a+b).

= 1

(Seca+tana) = 1

Seca+tana = 1/4   


BY adding (1) & (2), we get

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

Therefore

2seca = 17/4

Seca means the = 17/8  ---------- (3).


BY subtract (1) & (2), we get

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

Seca + tana - seca + tana = 15/4
 
2tana = 15/4

tana = 15/8   -


We know = sec theta/tan theta.


By solving (3) & (4), we get

cosec a =
$\frac{17}{8 \frac{15}{8} } = \frac{17}{15}$