Question

For which value of acute angle is cos θ / (1 − sin θ) + cos θ / (1 + sin θ) = 4 ture?
For which value of 0° < θ < 90°, above equation is not defined?

Answer 1

cosθ/(1 - sinθ) + cosθ/(1 + sinθ) = 4

=> {cosθ(1 + sinθ) + cosθ(1 - sinθ)}/(1 - sinθ)(1 + sinθ) = 4

=> {cosθ + cosθ.sinθ + cosθ - cosθ.sinθ}/(1 - sin²θ) = 4

=> 2cosθ/cos²θ = 4 [ we know, sin²x + cos²x = 1 so, (1 - sin²θ) = cos²θ]

=> 2/cosθ = 4

=> cosθ = 1/2 = cos60°

hence, in 0 < θ < 90° , θ = 60°

now, if given equation is not defined.
(1 - sinθ) = 0
in 0 < θ < 90° , sinθ = 1 at 90°
hence, equation is undefined at θ = 90°

[ note : one more case for undefined, (1 + sinθ) = 0 , but in 0 < θ < 90° it's not possible. thars why I didn't mention it above]

Answer 2

Answer:

Step-by-step explanation:cosθ/(1 - sinθ) + cosθ/(1 + sinθ) = 4

=> {cosθ(1 + sinθ) + cosθ(1 - sinθ)}/(1 - sinθ)(1 + sinθ) = 4

=> {cosθ + cosθ.sinθ + cosθ - cosθ.sinθ}/(1 - sin²θ) = 4

=> 2cosθ/cos²θ = 4 [ we know, sin²x + cos²x = 1 so, (1 - sin²θ) = cos²θ]

=> 2/cosθ = 4

=> cosθ = 1/2 = cos60°

hence, in 0 < θ < 90° , θ = 60°

now, if given equation is not defined.

(1 - sinθ) = 0

in 0 < θ < 90° , sinθ = 1 at 90°

hence, equation is undefined at θ = 90°

[ note : one more case for undefined, (1 + sinθ) = 0 , but in 0 < θ < 90° it's not possible. thars why I didn't mention it above]