Question

Csc2x + sec2x = csc2x sec2x?

Answer 1

As proved below.

Explanation:

Sum must be `csc^2 x + sec^2 x = csc^2x sec^2x`

`sec x = 1/cos x, csc x = 1/ sin x`

`L H S = csc^2 x + sec^2 x`

`=> 1 / sin^2 x + 1 / cos ^2 x`

`=> (cos^2 x + sin^2 x) / (sin^2x cos^2 x), " taking L C M"`

`=> 1 / (sin^2 x cos^2 x), " as " sin^2x + cos^2x = 1`

`color(crimson)(=> csc^2 x sec^2 x = R H S`