IDNLearn.com offers a user-friendly platform for finding and sharing knowledge. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.
Sagot :
[tex]cscx=\frac{1}{sinx};\ sin^2x+cos^2x=1\to cos^2x=1-sin^2x\\----------------------------\\\\csc^2xcos^2x=csc^2x-1\\\\L=csc^2xcos^2x=\frac{1}{sin^2x}\cdot cos^2x=\frac{cos^2x}{sin^2x}\\\\R=csc^2x-1=\frac{1}{sin^2x}-1=\frac{1}{sin^2x}-\frac{sin^2}{sin^2x}=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}\\\\\boxed{L=R}[/tex]
[tex]LHS\\ \\ ={ cosec }^{ 2 }\theta { cos }^{ 2 }\theta \\ \\ ={ cosec }^{ 2 }\theta \left( 1-{ sin }^{ 2 }\theta \right)[/tex]
[tex]\\ \\ ={ cosec }^{ 2 }\theta -{ cosec }^{ 2 }\theta { sin }^{ 2 }\theta \\ \\ ={ cosec }^{ 2 }\theta -\frac { 1 }{ { sin }^{ 2 }\theta } \cdot { sin }^{ 2 }\theta [/tex]
[tex]\\ \\ ={ cosec }^{ 2 }\theta -1\\ \\ =RHS[/tex]
[tex]\\ \\ ={ cosec }^{ 2 }\theta -{ cosec }^{ 2 }\theta { sin }^{ 2 }\theta \\ \\ ={ cosec }^{ 2 }\theta -\frac { 1 }{ { sin }^{ 2 }\theta } \cdot { sin }^{ 2 }\theta [/tex]
[tex]\\ \\ ={ cosec }^{ 2 }\theta -1\\ \\ =RHS[/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.
