Question

solve this trigonometry question​

Answer 1

please solve similar question to these

Answer 2

Hello mate!


Answer:


(p² + 1)/p² - 1


Step-by-step explanation:


Given:

sec θ + tan θ = p   ----- (i)


We know that sec²θ - tan²θ = 1


⇒ (secθ + tanθ)(secθ - tanθ) = 1


⇒ (p)(secθ - tanθ) = 1


⇒ secθ - tanθ = (1/p)   ----- (ii)


On solving (i) & (ii), we get


⇒ secθ + tanθ + secθ - tanθ = p + 1/p


⇒ 2secθ = p² + 1/p


⇒ secθ = (p² + 1)/2p


⇒ cosθ = (1/secθ)


            = 2p/p² + 1

Sin²θ = 1 - cos²θ


         = 1 - (2p/p² + 1)²


         = 1 - (4p²)/p⁴ + 1 + 2p²


         = (p⁴ + 1 + 2p² - 4p²)/p⁴ + 1 + 2p


         = (p⁴ + 1 - 2p²)/p⁴ + 1 + 2p


         = (p² - 1)²/(p² + 1)²


sin θ= p² - 1/p² + 1.

Now,


We know that cosecθ = (1/sinθ)


⇒ (p² + 1)/p² - 1.


Thank you!

Hope it helps!

Please mark it as brainliest! If it helped