Question

if cosecant theta + cot theta is equal to P then prove that cos theta is equal to p square minus one upon p square + 1​

Answer 1

Answer:

Step-by-step explanation:

cosecθ + cotθ = P  =====> Equation 1.

we know, cosec²θ - cot² θ  = 1

= > (cosecθ  + cotθ )( cosecθ - cotθ)= 1

=> (cosecθ - cotθ ) × P = 1

=>  cosecθ - cotθ = 1/P ========> Equation 2

Let's solve (i ) and (ii)

cosecθ + cotθ = P  =====> Equation 1

cosecθ - cotθ = 1/P ========> Equation 2

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//by adding both equations cotθ cancels out

=> 2cosecθ = P + 1/P

=> Cosecθ = (1+ P²) / 2P

//by subtracting 2 from 1, cosecθ cancels out

=> 2 cotθ = P - 1/P

=> Cotθ = (P² -  1) / 2P  

cotθ/ cosecθ= (P²-1/ 2P) × (2P/P²+1)

cosθ = P²-1/P²+1

Hence proved