Question

B) (1 - cos B)(1 + cos B) =
1/cosec^2(B)

Answer 1

Proved

Explanation:

`(1-cosB)(1+cosB)=(1)/(cosec^2B) \\\\Use\\\\ (a+b)(a-b)=a^2-b^2 ,\\so,\\=(1)^2-(cosB)^2\\=1-cos^2B\\\\Now\ , we\ know\ \\sin^2B+cos^2B=1\\\\so,\\sin^2B=1-cos^2B\\so we just replace,\\\\=1-cos^2B=>sin^2B\\and\ since\ sinB=(1)/(cosecB) \\\\=sin^2B=>(1)/(cosec^2B)\\`