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

Answer:

Step-by-step explanation:

Cosθ/(1 - sinθ) + cosθ/(1 + sinθ) = 4 (Given)

Simplifying,

= Cosθ(1 + sinθ) + cosθ(1 - sinθ) /(1 - sinθ)(1 + sinθ) = 4

= Cosθ + cosθ × sinθ + cosθ - cosθ.sinθ} / (1 - sin²θ) = 4

Since, sin²x + cos²x = 1 therefore, (1 - sin²θ) = cos²θ

= 2cosθ/cos²θ = 4

= 2/cosθ = 4

= cosθ = 1/2

= cos 60°

Thus, when 0 < θ < 90° , then θ = 60°

If the given equation is not defined, ie. (1 - sinθ) = 0

in 0 < θ < 90° , sinθ = 1 at 90°

Then the equation is undefined at θ = 90°.

Answer 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

Cosθ/(1 - sinθ) + cosθ/(1 + sinθ) = 4 (Given)

Simplifying,

= Cosθ(1 + sinθ) + cosθ(1 - sinθ) /(1 - sinθ)(1 + sinθ) = 4

= Cosθ + cosθ × sinθ + cosθ - cosθ.sinθ} / (1 - sin²θ) = 4

Since, sin²x + cos²x = 1 therefore, (1 - sin²θ) = cos²θ

= 2cosθ/cos²θ = 4

= 2/cosθ = 4

= cosθ = 1/2

= cos 60°

Thus, when 0 < θ < 90° , then θ = 60°

If the given equation is not defined, ie. (1 - sinθ) = 0

in 0 < θ < 90° , sinθ = 1 at 90°

Then the equation is undefined at θ = 90°.