Question

cosA/1-sinA=1+sinA/cosA​

Answer 1

Solution:-

$\rm \implies \: \dfrac{ \cos A}{1 - \sin A } = \dfrac{1 + \sin A}{ \cos A}$

Using Cross multiplication methods

$\rm \implies \: ( \cos A)( \cos A) = (1 - \sin A)(1 + \sin A)$

Now use this identity

$\rm \implies(a - b )(a + b) = {a}^{2} - {b}^{2}$

We can write

$\rm \implies \cos ^{2} A = 1 - \sin ^{2} A$

$\rm \implies \cos ^{2} A + \sin ^{2} A = 1$

We know that

$\rm \implies \cos ^{2} \theta + \sin ^{2} \theta = 1$

Put the value

$\rm \implies \cos ^{2} A + \sin ^{2} A = 1$

$\rm \implies 1= 1$

Hence proved

More identities

$\rm \to \tan \theta = \dfrac{ \sin \theta }{ \cos\theta}$

$\rm \to \: \cos( \theta) = \dfrac{ \cos( \theta) }{ \sin( \theta) }$