Question

prove that :-

secA -1 / secA +1=sin²A/(1+cos)²​

Answer 1

Solution:-

$\implies\sf\ \dfrac{secA-1}{secA+1}= \dfrac{sin^2A}{(1+cosA)^2}\\ \\ \\ taking\ LHS\\ \\ :\implies\sf\ Multiplying\ both\ Numerator\ and\ denominator\ by\ secA+1\\ \\ :\implies\sf\ \dfrac{secA-1}{secA+1}\times\dfrac{secA+1}{secA+1}\\ \\ :\implies\sf\ \dfrac{sec^2A-1}{(secA+1)^2}\\ \\ :\implies\sf\ \ \dfrac{tan^2A}{(1/_{cosA}+1)^2}\\ \\ :\implies\sf\ \dfrac{tan^2A}{^{(1+cosA)^2}/_{cos^2A}}\\ \\ :\implies\sf\ \dfrac{^{sin^2A}/_{cos^2A}}{^{(1+cosA)^2}/_{cos^2A}}\\ \\ :\implies\sf\ \dfrac{sin^2A}{\cancel{cos^2A}}\times\ \dfrac{\cancel{cos^2A}}{(1+cosA)^2}\\ \\ :\implies\pink{\sf\ \ \dfrac{sin^2A}{(1+cosA)^2}}\ \ \ \sf\ Hence\ Proved !!$

Answer 2

Answer:

Compressibility is the measure of how much a given volume of matter decreases when placed under pressure. If we put pressure on a solid or a liquid, there is essentially no change in volume. The kinetic-molecular theory explains why gases are more compressible than either liquids or solids.