Question

if cosectheta +cottheta=p then what is sectheta​

Answer 1

Answer:

Secθ = p²+1 /p²-1

Step-by-step explanation:

cosecθ+cotθ=p

1/sinθ+cosθ/sinθ=p

1+cosθ/sinθ=p

=> SQUARING ON BOTH SIDES

= (1+COSθ)²/(SINθ)²= P²

= (1+ Cosθ)² / (Sinθ)² = P²

= (1+cosθ)² = (p²)[(Sinθ)²]

= (1+ cosθ) ² = (p²) [(1-cos²θ)]

= (1+ cosθ) ² = (p²) [ (1+cosθ)(1-cosθ) ]

= (1+cosθ)² ÷ (1+ cosθ) = (p²)[(1-cosθ)]

= 1+cosθ = (p²)[1-cosθ]

= 1+cosθ ÷ 1-cosθ = p²

= Here, Using (a+b/a-b=c+d/c-d). This is known as Componendo and dividendo

According to the Question statement!

1+cosθ ÷ 1-cosθ= p²

Then,

(1+cosθ) + (1 - cosθ) ÷ (1+ Sinθ - (1-sinθ) = p²+1 / p²-1

= 2/2cosθ = p²+1/p²-1

= 1/cosθ = p²+1/p²-1

= Secθ = p²+1 /p²-1