Question

prove that: cos theta/ 1- sin theta+ cos theta/ 1+sin theta= 4

Answer 1

Answer:

Refer the attachment for your answer.

Answer 2

Answer:

${ \large{ \underline{ \sf{Correct \: Question}}}}$

Find the value of theta when,

${ \sf{ \frac{cos \theta}{1 - sin \theta} + \frac{cos \theta}{1 + sin \theta} = 4}}$

${ \large{ \underline{ \sf{Solution}}}}$

By taking LCM,

$: { \longmapsto{ \sf{ \frac{(1 + Sin \theta)Cos\theta+(1 - Sin \theta)(Cos\theta}{(1+Sin\theta)(1-Sin\theta)} =4}}}\\\\ : { \longmapsto{ \sf{ \frac{Cos\theta+ Sin\theta Cos\theta+(Cos\theta-Sin\theta Cos\theta)}{ {1}^{2} - {Sin}^{2}\theta } =4}}}\\\\ : { \longmapsto{ \sf{ \frac{Cos\theta+Sin\theta Cos\theta+Cos\theta-Sin\theta Cos\theta}{1- {Sin}^{2} \theta } =4}}}\\\\ : { \longmapsto{ \sf{ \frac{Cos\theta + Cos\theta}{ {Cos}^{2}\theta } =4}}}\\\\ : { \longmapsto{ \sf{ \frac{2Cos\theta}{Cos\theta .Cos\theta}=4 }}}\\\\ :{\longmapsto{\sf{ \frac{2({\cancel{Cos\theta}})}{\cancel{Cos\theta}.Cos\theta}}}=4}\\\\:{\longmapsto{\sf{Cos\theta= \frac{2}{4} }}}\\\\:{\longmapsto{\sf{Cos\theta= \frac{1}{2} }}}\\\\:{\longmapsto{\sf{\bf{\theta=60°}}}}$