Question

If 15 tan^2θ + 4sec^2θ = 23, then find the value of (sec θ + cosec θ)^2 - sin^2θ

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\huge\fcolorbox{black}{teal}{Solution:-}$

✏️ Answer :-

★ The value of (secθ + cosecθ)² - sin²θ = 15/2

✏️ Step-by-step explanation :-

★ We have,

15 tan²θ + 4sec²θ = 23

⇒15 tan²θ + 4 (tan²θ + 1) = 23

[ ∵ sec²θ = 1 + tan²θ ]

⇒15 tan²θ + 4tan²θ + 4 = 23

⇒19tan²θ = 19

⇒tanθ = 1

⇒tanθ = tan 45°

⇒θ = 45°

Now,

(secθ + cosecθ)² - sin²θ = (sec 45° + cosec 45°)² - sin² 45°

= (√2 + √2)² - [1/√2]²

= (2√2)² - 1/2

= 8 - 1/2

= 15/2

[The required value!]

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I hope this helps! :)