Multiply and simplify sin x cos xsec x cot x sin x cos xsec

Multiply and simplify. sin x cos x(sec x + cot x) sin x cos x(sec x + cot x) =

Solution

sin x cos x (sec x + cot x)

= sin x cos x ( 1/cosx + cosx / sin x) [ Since sec x = 1/cos x and cotx = cos x / sin x ]

Now, we distribute.

So, we get

= (sin x cos x ) / cos x + (sin x cos x ) (cos x / sin x)

= sin x + cos²x (Answer)