Question

Show that tan theta + sec theta - one / tan theta - sec theta + one = one - sin theta / cos theta

Answer 1

Answer:

your answer attached in the photo

Answer 2

Answer:

Hey Mate,

We have to prove LHS = RHS

LHS =

RHS =

Lets Start from LHS

LHS =

=  

=

=

=

=

= = RHS

Hence Proved,

LHS=RHS

4.3

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Comments Report

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Here, i am holding the "THETAS" as "A".

So, we can proceed our solution as under :

(tan A + sec A - 1)/(tan A - sec A + 1)

= (tan A + sec A - sec²A + tan²A)/(tan A - sec A + 1)

= [tan A + sec A - {(sec A+tan A) (sec A - tan A)}]/[tan A - sec A + 1]

= [tan A + sec A (1 - sec A + tan A)]/(tan A - sec A + 1)

= tan A + sec A

= sin A/cos A + 1/cos A

= ( 1 + sin A ) / cos A

=

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ULTIMATELY,

L.H.S. = R.H.S. (PROVED)