IIT JEE , AIEEE Forum - Mathematics , Trignometry - cosec

dhwanitmunshi

pls explain

if cosec

- cot

= q , then cosec

= ________
(a) q + 1/q
(b) q - 1/q
(c) 1/2(q + 1/q)
(d) 2(q+1/q)

nadeemoidu

cosecA-cotA=q......................(1)

but , (cosecA-cotA)(cosecA+cotA) =1 [identity]

q(cosecA+cotA) =1

(cosecA+cotA) =1/q..................(2)

add (1) and (2) , we get the answer as (c)

rabindra8

use the formula cosec²

-cot²

=1 and find out your required answer.

and i.e. cosec

= (q²+1)/2q

Aastha_faith

Cosec x =1/sin x

Cot x = cos x/sin x

Cosec x ? cot x = (1-cos x)/sin x

=>1-cos x = p sin x

P+1/p = (1-cos x)/ sin x + sin x /1-cos x

_____= [1+cos² x ? 2 cos x + sin² x] / (sin x) (1-cos x) ------------by taking LCM

_____= [1+1-2 cos x] / (sin x) (1-cos x) ----------since sin² x+ cos² x =1

_____= [2-2 cos x] / (sin x) (1-cos x) -------by taking ?2? common

_____= 2{1-cos x}/ (sin x) (1-cos x) -------- (1-cos x) in numerator & denominator

_____= 2 / sin x

_____= 2 cosec x

Therefore, cosec x = ½ (p + 1/p)

Aastha_faith