Question

please give the solution ...NO SPAMMERS ! 10 POINTS ...THE FASTEST AND CORRECT ANS WILL GET A BRAINLIEST​

Answer 1

here's your answer!!

Answer 2

$\bf{\huge{ \red{ \underline{ \underline{Solution:}}}}} \\ \\ \rm {Q: \dfrac{tan^2 \: A}{(sec \: A - 1)^2} = \dfrac {(1 + cos \: A)}{(1 - cos \: A) }} \\ \\ \rm { \green{ \underline{Considering \: \: R.H.S:}}} \\ \\ \rm {\dfrac{(1 + cos \: A)}{(1 - cos \: A)} }\\ \\ \rm {Multiplying \: \: sec \: A \: \: with \: \: both \: \: numerator \: \: and \: \: denominator.} \\ \\ \rm {\dfrac{(sec \: A + 1)}{(sec \: A - 1)} }\\ \\ \rm {Multiplying \: \: (sec \: A - 1) \: \: with \: \: both \: \: numerator \: \: and \: \: denominator.} \\ \\ \rm {\dfrac{(sec \: A + 1) \: (sec \: A - 1)} { (sec \: A - 1) \: (sec \: A - 1)}} \\ \\ \rm {\dfrac{(sec^2 \: A - 1)} { (sec \: A - 1)^2}} \\ \\ \rm {Here, \: \: R.H.S = L.H.S} \\ \\ \rm {Hence, \: \: Proved.} \\ \\ \rm { \underline{ \blue{Algebraic \: \: Identities \: \: used:}}} \\ \\ \rm {(a + b) (a - b) = a^2 - b^2} \\ \\ \rm {(a - b) (a - b) = (a - b)^2} \\ \\ \\ \rm { \underline{ \blue{Trigonometric \: \: Identities \: \: used:}}} \\ \\ \rm{sec \: A \times cos \:A = 1} \\ \\ \rm {(sec^2 \: A - 1) = tan^2 \: A}$