Question

sin theta -cos theta plus one / sin theta plus cos theta minus one is equal to one divided by sec theta minus tan theta

Answer 1

Answer:

Step-by-step explanation:

sinФ - cosФ + 1/ sinФ + cosФ - 1

=Multiplying Numerator and Denominator by ( 1 - sinФ), we get

( 1 - sinФ)*(sinФ - cosФ + 1)/(sinФ + cosФ - 1)*( 1 - sinФ),

Simplifying Numerator we get,

(sinФ - cosФ + 1 -sin²Ф + sinФcosФ - sinФ )/(sinФ + cosФ - 1)*( 1 - sinФ)

=(-cosФ + cos²Ф + sinФcosФ )/(sinФ + cosФ - 1)*( 1 - sinФ),

Now, taking cosФ  in common out of Numerator, we get

=cosФ *(-1 + cosФ  + sinФ )/(sinФ + cosФ - 1)*( 1 - sinФ)

= cosФ / 1 - sinФ,

Now, Dividing Numerator and Denominator by cosФ , we get

= 1/secФ-tanФ.