If cosecθ−cotθ = 1/4 then the value of cosecθ + cotθ is ___
Answers
Answer:
cosecθ + cotθ =4
Step-by-step explanation:
cosecθ−cotθ = 1/4
w.k.t,
the value of cosec^2θ - cot^2θ=1
(x+y)(x-y)=x^2-y^2
in the same way
(cosecθ−cotθ)(cosecθ + cotθ)=1
1/4(cosecθ + cotθ)=1
cosecθ + cotθ=4
Step-by-step explanation:
cosec - cot = 1/4
1/ sin - cos / sin = 1/4
(1-cos )/sin = 1/4
cross multiply
4 ( 1-cos) = sin
squaring both sides
16 ( 1+cos^2 - 2cos) = sin ^2
16 + 16 cos ^ 2 - 32 cos = 1- cos ^2
17 cos ^ 2 - 32 cos + 15 = 0
17 cos ^ 2 - 17 cos - 15 cos + 15 = 0
17 cos ( cos -1) -15 ( cos -1) = 0
( 17 cos -15) ( cos -1) = 0
cos = 15/17 or 1
cos = base / hypo = 15/17
p =√ hypo ^2 - base ^2
p = √ 289 - 225
p = √ 64 = 8
cosec = hypo / prep = 17/8
cot = base / prep = 15/8
cosec + cot = 32/8 = 4
if we take cos = 1 then
cosec = not defined so we can leave this