Question

if sec theta+ tan theta =p then find the value of sin theta in terms of p.​

Answer 1

Answer:

p²-1

Step-by-step explanation:

sec theta +tan theta =p_______ 1

sec theta - tan theta=1/p______2

1-2

2 tan theta=p²-1/p

tan theta =p²-1/2p

tan theta =sin theta/cos theta

comparing on both sides

sin theta=p²-1

Answer 2

EXPLANATION.

⇒ secθ + tanθ = p. - - - - - (1).

As we know that,

Formula of :

⇒ 1 + tan²θ = sec²θ.

⇒ sec²θ - tan²θ = 1.

⇒ (x² - y²) = (x - y)(x + y).

Using this formula in the equation, we get.

⇒ (secθ - tanθ)(secθ + tanθ) = 1.

Put the value in the equation, we get.

⇒ (secθ - tanθ)(p) = 1.

⇒ secθ - tanθ = 1/p. - - - - - (2).

From equation (1) & (2), we get.

⇒ secθ + tanθ = p. - - - - - (1).

⇒ secθ - tanθ = 1/p. - - - - - (2).

Adding both the equation, we get.

⇒ 2secθ = p + 1/p.

⇒ 2secθ = (p² + 1)/p.

⇒ secθ = (p² + 1)/2p.

⇒ secθ = 1/cosθ.

⇒ cosθ = (2p)/(p² + 1).

As we know that,

⇒ cosθ = Base/Hypotenuse = (2p)/(p² + 1).

By using Pythagoras theorem, we get.

⇒ H² = (Perpendicular)² + B².

⇒ [(p² + 1)]² = (Perpendicular)² + (2p)².

⇒ [p⁴ + 1 + 2p²] = (Perpendicular)² + 4p².

⇒ p⁴ + 1 + 2p² - 4p² = (Perpendicular)².

⇒ p⁴ - 2p² + 1 = (Perpendicular)².

⇒ (1 - p²)² = (Perpendicular)².

⇒ (Perpendicular) = (1 - p²).

⇒ sinθ = Perpendicular/Hypotenuse.

⇒ sinθ = (1 - p²)/(1 + p²).

                                                                                                                           

MORE INFORMATION.

(1) = sin²θ + cos²θ = 1.

(2) = 1 + tan²θ = sec²θ.

(3) = 1 + cot²θ = cosec²θ.