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-BARSIC- [3]
3 years ago
9

How do I simplify (tanx/1+secx) + (1+secx/tanx)

Mathematics
1 answer:
Ket [755]3 years ago
8 0
Tan x /(1 +sec x) + (1+sec x) /tan x

Tan x=sin x / cos x
1+ sec x=1 +1/cos x=(cos x+1)/cos x

Therefore:
tan x /(1 +sec x) =(sin x/cos x)/(cos x+1)/cos x=
=(sin x * cos x) / [cos x* (cos x+1)]=sin x /(Cos x+1)

(1+sec x) /tan x=[(cos x+1)/cos x] / (sin x/cos x)=
=[cos x(cos x+1)]/(sin x *cos x)=(cos x+1)/sin x

tan x /(1 +sec x) + (1+sec x) /tan x=
=sin x /(Cos x+1) + (cos x+1)/sin x=
=(sin²x+cos²x+2 cos x+1) / [sin x(cos x+1)]=

Remember: sin²x+cos²x=1⇒ sin²x=1-cos²x

=(1-cos²x+cos²x+2 cos x+1) / [sin x(cos x+1)]=
=2 cos x+2 /  [sin x(cos x+1)]=
=2(cos x+1) /  [sin x(cos x+1)]=
=2 /sin x

Answer : tan x /(1 +sec x) + (1+sec x) /tan x= 2/sin x
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8 0
3 years ago
PLEASE HELP, WILL GIVE BRAINLIEST!!!<br><br><br> Find the inverse of f(x)=6x-4<br> and find f^-1(62)
Lena [83]
Answer: 11

=========================

Explanation:

To find the inverse, or f^-1 of a function, you first replace the y= 6x-4 with x=6y-4

Finding the inverse from here is basically just finding y in terms of x.

1) x=6y-4
2) x+4=6
3) (x+4)/6= y

y= (x+4)/6 is now your f^-1.

Now that you have your inverse, replace 62 with your x in y=(x+4)/6

1) (62+4)/6
2) 66/6
3) 11

Therefore, f^-1(62)= 11

Hope this helps :)
5 0
2 years ago
Read 2 more answers
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