Question

if y=(1/tanx)+(1/cotx) then f'(x) is??

Answer 1

f(x)=sin

−1

(tanx)+cos

−1

(cotx)

=tan

−1

(

1−tan

2

x

tanx

)+tan

−1

(

cotx

−1−cot

2

x

)

=tan

−1

(

1−tan

2

x

tanx

)+tan

−1

(

tanx

tan

2

x−1

)

As inside square root, quantity ≥0

⇒1−tan

2

x>0 and tan

2

x−1>0

⇒tan

2

x≤1 and tan

2

x≥1

⇒tan

2

x=1⇒tanx=±1

⇒x=nπ±π/4

f(x)=π/2+0=π/2

As f(x)=π/2 at π/4,3π/4,5π/4...⇒ Period =π/2

As f(π/4)=f(3π/4)=π/2⇒f is many - one

⇒ All are correct