Question

If cosec theta + cot theta = 5, then evaluate sec theta

Answer 1

Answer:

we know that

Step-by-step explanation:

cosec²theta -cot ²theta

Answer 2

Answer:

Secθ = -1 or 1.08(approx)

Step-by-step explanation:

In this question

We have been given that

Cosecθ + Cotθ = 5

Then we need to find the value of Secθ

Changing Cosecθ and Cotθ into Sinθ and Cosθ

Now, $\frac{1}{Sin\theta}\ +\ \frac{Cos\theta}{Sin\theta}\ =\ 5$

$\frac{1+Cos\theta}{Sin\theta}\ =\ 5$

Cross Multiplying we get,

1 + Cosθ = 5Sinθ

Squaring both the sides we get,

$(1\ +\ Cos\theta)^{2}\ =\ 25Sin^{2}\theta$

$1\ +\ Cos^{2}\theta\ +\ 2Cos\theta\ =\ 25Sin^{2}\theta$

$1\ +\ Cos^{2}\theta\ +\ 2Cos\theta\ =\ 25(1-Cos^{2}\theta)$

$1\ +\ Cos^{2}\theta\ +\ 25Cos^{2}\theta\ +\ 2Cos\theta\ -25\ =\ 0$

$26Cos^{2}\theta\ +\ 2Cos\theta\ -\ 24\ =\ 0$

Using Shridhanacharya formula we get,

Here a = 26 ; b = 2 ; c = -24

Cosθ = $\frac{-2\ \pm\ \sqrt{(2)^{2}\ -\ 4\times 26\times (-24)}}{2\times 26}$

Cosθ = $\frac{-2\ \pm\ \sqrt{4\ + 2496}}{52}$

Cosθ = $\frac{-2\ \pm\ \sqrt{2500}}{52}$

Cosθ = $\frac{-2\ \pm\ 50}{52}$

Cosθ = $\frac{-2\ +\ 50}{52}$ and $\frac{-2\ -\ 50}{52}$

Cosθ = $\frac{48}{52} and [tex]\frac{-52}{52}$

Therefore we know that Secθ = $\frac{1}{Cos\theta}$

Hence Secθ = $\frac{52}{48}$ and $\frac{52}{-52}$

Secθ = 1.08 and 1