Question

if cosec theta + cot theta is equal to K then prove that cos theta is equal to K square - 1 / square + 1​

Answer 1

Step-by-step explanation:

given that

K= cosecA+cotA

Prove that

(k^2 -1 )/( k^2 + 1 )= cosA

Equations used for solve the problem

Cosec ^A - 1 = Cot ^A

Cot ^A + 1 = Cosec ^ A

Cosec A = 1/SinA

Cot A = CosA/SinA

Answer 2

given

$\cosec \theta + \cot \theta = k$

Now RHS

$\frac{ {k}^{2} - 1}{ {k}^{2} + 1} \\ \\ = \frac{( {cosec \theta + \cot \theta})^{2} - 1}{( {cosec \theta + cot \theta})^{2} + 1} \\ \\ = \frac{2 {cot}^{2} \theta + 2cosec \theta cot \theta}{2 {cosec}^{2} \theta + 2cosec \theta cot \theta }$

$= \frac{2cot \theta(cot \theta + cosec \theta)}{2coec \theta(cosec \theta + cot \theta)} \\ \\ = \frac{cot \theta}{cosec \theta} \\ \\ = cos \theta$