Question

answer the question

Answer 1

let sin2X = 2sinX × cosX
and use sin^2X+cos^2x=1

LHS=sinX-✓sin^2X+cos^2X+2sinX cosX
-----------------------------------------------
cosX -✓ sin^2X+cos^2X+2sinX cosX


= sinX-✓ (sinX+CosX)^2
-----------------------------
cosX-✓(sinX+CosX)^2

= sinX-sinX-cosX
----------------------
cosX -sinx-cosx

= -cosX
----------
-sinX

= cotX. ( where X = theta)