if y=(1/tanx)+(1/cotx) then f'(x) is??
Answers
Answered by
48
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
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