if y=sin²x/1+cot x + cos²x/1+tan x then dy /dx is equal to (A) COS 2x (C) 2 cos² x (B) -cos 2x (D) cos³ x
please give step explanation
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Step-by-step explanation:
Given, y=
1+cotx
sin
2
x
+
1+tanx
cos
2
x
=
sinx+cosx
sin
3
x
+
sinx+cosx
cos
3
x
=
cosx+sinx
(sinx+cosx)(sin
2
x+cos
2
x−sinxcosx)
y(x)=1−
2
sin2x
⇒y
′
(x)=−cos2x
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