if cosectheta +cottheta=p then what is sectheta
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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
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