16 sin theta = 32 cos theta, find the value of sec theta and cosec theta.
Answers
Step-by-step explanation:
16 sin theta = 32 cos theta
sin theta / cos theta = 2
tan theta = 2
perpendicular = 2
base = 1
hypotenuse =√3
sec theta = √3
cosec theta = √(3)/2
Step-by-step explanation:
16 sin theta = 32 cos theta
sin theta / cos theta = 32 / 16
tan theta = sin theta / cos theta
therefore,
tan theta = 32 / 16
tan theta = 2 / 1
tan^2 theta = sec^2 theta - 1
(2 / 1)^2 = sec^2 theta - 1
sec^2 theta = 1 + (2 / 1)^2
sec^2 theta = 1 + (4 / 1)
sec^2 theta = 1 + 4 / 1
sec^2 theta = 5 / 1
sec theta = √5 / 1
sec theta = √5 ÷ 1
inverse of tan theta = cot theta
therefore,
cot theta = 1 / 2
cosec^2 theta = 1 + cot^2 theta
cosec^2 theta = 1 + (1 / 2)^2
cosec^2 theta = 1 + (1 / 4)
cosec^2 theta = 4 + 4 / 1
cosec^2 theta = 8 / 1
cosec^2 theta = √(8 / 1
cosec^2 theta =√4 × 2 / 2
cosec^2 theta =2√2 / 2
cosec^2 theta =√2 / 1
cosec^2 theta =√2