Question

if cosec theta+cot theta=q, show that cosec theta-cot theta=1/q hence find the values of sin theta and sec theta

Answer 1

Step-by-step explanation:

hope this will help you

Answer 2

Answer:

• sinθ = 2q/(1 + q²)
• secθ = 1/cosθ = (q² + 1)/(q² - 1)

Step-by-step explanation:

GIVEN:-

cosecθ + cotθ = q ------------ ( 1 )

we have to prove

cosecθ - cotθ = 1/q

from ------ ( 1 )

cosecθ + cotθ = q

=> 1/q = 1/(cosecθ + cotθ)

=> 1/q = 1/(cosecθ + cotθ) × (cosecθ - cotθ)/(cosecθ - cotθ)

=> 1/q = (cosecθ - cotθ)/(cosec²θ - cot²θ)

[ cosec²θ - cot²θ = 1 trig. Identity]

=> 1/q = (cosecθ - cotθ)/1

=> 1/q = (cosecθ - cotθ) -------- ( 2 )

we have to find the value of sinθ and secθ

on adding ------( 1 ) & ------ ( 2 )

(cosecθ + cotθ) + (cosecθ - cotθ) = q + 1/q

=> 2cosecθ = (q² + 1)/q

=> 2/sinθ = (q² + 1)/q

=> sinθ = 2q/(1 + q²)

from ------( 1 ) & ------( 2 )

(cosecθ + cotθ) - (cosecθ - cotθ) = q - 1/q

=> 2cotθ = (q² - 1)/q

=> 2cosθ/sinθ = (q² - 1)/q

[putting value of sinθ]

=> 2cosθ = (q² - 1)/q × 2q/(1 + q²)

=> cosθ = (q² - 1)/(q² + 1)

=> secθ = 1/cosθ = (q² + 1)/(q² - 1)

thanks,

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