Step-by-step explanation:
cot x + 2 tan x + tan³ x
Write in terms of sine and cosine:
(cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)
Find the common denominator:
(cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))
Add:
(cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)
Factor:
(sin² x + cos² x)² / (sin x cos³ x)
Pythagorean identity:
1 / (sin x cos³ x)
Multiply top and bottom by cos x:
cos x / (sin x cos⁴ x)
Simplify:
cot x sec⁴ x
1) f(x)=2x
when x=3 then f(x) =3×2=<em><u>6</u></em>
when x=4 then f(x)=4×2=<em><u>8</u></em>
2)At y=35(no. of mangoes),x corresponds to y=60(amount)
so$<em><u>6</u></em><em><u>0</u></em><em><u>,</u></em><em><u> </u></em><em><u>amount</u></em><em><u> </u></em><em><u>he</u></em><em><u> </u></em><em><u>need</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>spend</u></em><em><u>!</u></em>
3) f(x)= x+2
for x=1, f(x)=1+2=<em><u>3</u></em>
for x=2,f(x)=2+2=<em><u>4</u></em>
✌️:)