Question

i)The angle á lies between 0 and 90 and is such that 2tan sqaure á + sec square á=5-4tan á. show that
3tan square á +4taná-4=0
and hence find the exact value of taná
ii)It is give that the angle â is such that cot(á+â) = 6.Without using a calculator, find the exact value of cot â
i couldnot sole (ii)

Answer 1

2tan^2(x) + sec^2(x) = 5 - 4tan(x)
2tan^2(x) + 1+tan^2(x) = 5 - 4tan(x)
3tan^2(x) + 4tan(x) - 4 = 0
(tanx+2)(3tanx-2) = 0
Now you know tan(x)

cot(a+b) = 6
(cota*cotb-1)/(cota+cotb) = 6
cota = -2, so
(-2cotb-1)/(-2+cotb) = 6
-12cotb-6 = -2+cotb
-4 = 13cotb
cotb = -4/13

or, use cota = 2/3