Find x from the following equations:

⇒ cosec (90° + θ) +x cos θ cot (90° + θ) = cos θ

We know that when n is odd, cot → tan.

⇒ sec θ +x cos θ [-tan θ] = cos θ

⇒ sec θ –x cos θ tan θ = cos θ

⇒ sec θ –x cos θ (sin θ/ cos θ) = cos θ

⇒ sec θ –x sin θ = cos θ

⇒ sec θ – cos θ =x sin θ

We know that 1 – cos² θ = sin² θ

⇒ tan θ =x

∴x = tan θ