Question

tanФ + 1 ÷ tanФ=secФ × cosecФ

Answer 1

Answer:

p = tanФ + secФ

p - secФ = tanФ

p² + sec²Ф - 2 p secФ = tan²Ф = sec²Ф - 1

So secФ = (p² + 1) / 2p

so cosФ = 2p/(1+p²)

sinФ = √[1 - cos²Ф ] = (p²-1)/(1+p²)

cosec (Ф) = (1+p²)/(p²-1)

Answer 2

$\tan\alpha + \frac{1}{ \tan\alpha } \\ \\ = > \tan\alpha + \cot \alpha \\ \\ = > \frac{ \sin \alpha }{ \cos \alpha } + \frac{ \cos \alpha }{ \sin \alpha } \\ \\ = > \frac{ { \sin}^{2} \alpha + { \cos}^{2} \alpha }{ \cos \alpha \sin \alpha } \\ \\ = > \frac{1}{ \cos \alpha \sin \alpha } \\ \\ = > \frac{1}{ \cos \alpha } . \frac{1}{ \sin \alpha } \\ \\ = > \sec \alpha . \csc \alpha = R.H.S.$

HENCE PROVED ✔️✔️

@ItsChampion ✌️