Question

If Tan A+1/tanA =2 then the value of cosec A

Answer 1

Answer:

cosec A = ∞

Step-by-step explanation:

Here, I'll be using x instead of A for simplicity.

$\tan(x) + \frac{1}{ \tan(x) } = 2$

$\frac{ { \tan}^{2}(x) + 1 }{ \tan(x) } = 2$

$\frac{ { \sec }^{2}(x) }{ \tan(x) } = 2$

$\frac{1}{ \sin(x). \cos(x) } = 2$

$2 \sin(x) . \cos(x) = 1$

$\sin( \frac{x}{2} ) = 1$

$\frac{x}{2} = 90$

$x = 180$

So,

$\cosec(180) = \frac{1}{0} = \infty$

Answer 2

Answer:

Cosec A = √2

Step-by-step explanation:

Tan A + 1/ Tan A = 2

Tan A + 1/ Tan A - 2 = 0

Tan²A + 1 - 2 Tan A = 0

(Tan A - 1)² = 0

On squaring both side

Tan A - 1 = 0

Tan A = 1

Tan A = Tan 45°. (Tan 45 = 1)

therefore value of A = 45

Cosec A = Cosec 45 = √2