Question

Solve these
I will mark as brainliest ​

Answer 1

1)

To prove:(sec∅+tan∅-1)/(tan∅-sec∅+1)=cos∅/(1-sin∅)

take LHS

=>we know,sec^2∅-tan^2∅=1,,,put this value in numerator...

=>[sec∅+tan∅-{sec^2∅-tan^2∅}]/(tan∅-sec∅+1)

=>[sec∅+tan∅-(sec∅+tan∅)(sec∅-tan∅)]/(tan∅-sec∅+1)

=>taking sec∅+tan∅ common from numerator,we get

{(sec∅+tan∅)(1-sec∅+tan∅)}/(tan∅-sec∅+1)}

=>1-sec∅+tan∅ will be cancelled out from numerator and denominator

we get as

sec∅+tan∅=LHS......i)

now,take RHS

=>Divide numerator and denominator ,by cos∅

=>1/(1/cos∅-sin∅/cos∅)

=>1/(sec∅-tan∅)

=>now,divide numerator and denominator by sec∅+tan∅

=>(sec∅+tan∅)(sec^2∅-tan^2∅)

=>sec∅+tan∅=RHS.....ii)

from i) and ii) we can say

LHS=RHS

{Hence proved}

{hope it helps}