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

December 24, 2021

By Maria

2 thoughts on “Question:-<br /><br />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<br /><b”

1. Answer:

   [tex]Sin θ = q – q(Cos θ)

   Sec θ = \frac{1}{q(Sin θ) – 1}[/tex]

   Step-by-step explanation:

   In attachment

   I tried that by my own

   I think u can understand

   Thank you giving an opportunity to help you…☺️

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2. 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 !

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