Question

Question:-

If cosec θ + cot θ = q, show that cosec θ – cot θ = 1/q and hence find the values of sin θ and sec θ


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Answer 1

Answer:

cosecθ + cotθ = p -------(1)

Now,

cosec²θ - cot²θ = 1

(cosecθ + cotθ)(cosecθ - cotθ) = 1

p(cosecθ - cotθ) = 1 ------[ from (1) ]

cosecθ - cotθ = 1/p ------(2)

So, cosecθ - cotθ = 1/p

HENCE PROVED

Now,

ADDING (1) and (2)

2cosecθ = p + 1/p = (p² + 1)/p

cosecθ = (p² + 1)/2p

sinθ = 2p/(p² + 1)

therefore, sinθ = 2p/(p² + 1) -----(3)

SUBTRACTING (1) and (2)

2cotθ = p - 1/p = (p² - 1)/p

cosθ/sinθ = (p² - 1)/2p

cosθ/{2p/(p² + 1)} = (p² - 1)/2p ------[ from (3) ]

cosθ = (p² - 1)/(p² + 1)

therefore, cosθ = (p² - 1)/(p² + 1)

HOPE IT HELPS !

Answer 2

Answer:

$Sin θ = q - q(Cos θ) </p><p>Sec θ = \frac{1}{q(Sin θ) - 1}$

Step-by-step explanation:

In attachment

I tried that by my own

I think u can understand

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