Question

prove cosec²A + sin²A = 2​

Answer 1

Step-by-step explanation:

sin²x,cosec²x both are posituve real no.s

but we know for any positive real no.s

AM≥GM

now,AM=sin²x+cosec²x. [since AM=a+b/2]

GM=√sin²x.cosec²x[ GM=√ab]

=√1=1

AM≥GM

so,sin²x+cosec²x/2≥1

sin²x+cosec²≥2

this can be written as

cosec²x+sin²x=2