Question

Plz solve this question, this question was from my 3rd unit test. ​

Answer 1

To Prove :

[((sinΦ)/(1+cosΦ))+((sinΦ)/(1-cosΦ)) ] = 2/sinΦ

Proof :

= LHS =

= )) [((sinΦ)/(1+cosΦ))+((sinΦ)/(1-cosΦ)) ]

=)) [(sinΦ)(1-cosΦ)+(sinΦ)(1+cosΦ)]/((1 + cosΦ)(1-cosΦ))

=)) [ sinΦ ((1+cosΦ) + (1 -cosΦ))]

/ (1² - cos²Φ)

=)) [ sinΦ (1 + cosΦ + 1 - cosΦ ) ]

/ (sin²Φ)

=)) [ sinΦ (2) ] / (sin²Φ)

=)) 2sinΦ / (sinΦ)²

=)) 2 / sinΦ

= RHS

formula used :

sin²Φ + cos²Φ = 1