Question

If cot theta is equal to 3 / 4 prove that under root sec theta minus cosec theta divided by sec theta + cosec theta is equal to 1 divided by root 7

Answer 1

Answer:

Step-by-step explanation:

GIVEN:- cotФ = 3/4

IN ∆ABC, <B = 90°

so, cotФ = 3/4 = base/height = BC/AB

hence, BC = 3 , AB = 4

now, [by Pythagoras theorem],

AC² = AB² + BC²

AC² = 4² + 3²

AC² = 16 + 9

AC = √25

AC = 5

∵ AC = 5 , BC = 3 , AB = 4.

now, IN triangle, ABC

sinФ = AB/AC, cosФ = BC/AC

SinФ = 4/5 , cosФ = 3/5

if sinФ = 4/5 ⇒cosecФ = 5/4

if cosФ = 3/5 ⇒secФ = 5/3.

now, L.H.S root sec-cosec /sec+cosec

root [5/3-5/4]/5/3+5/4

root [5/12]/[35/12]

root 5/35

root 1/7

1 /root7

thus, L.H.S = R.H.S.

hope it will be helpful ..please mark as brainlist ..

Answer 2

Refers to attachment ♡~