If acot θ = b, then what will be the value of $$\frac{\text{b}\space\text{cos}\space\text{θ}-{\text{a}\space\text{sin}\space\text{θ}}}{{\text{b}\space\text{cos}\space\text{θ}+{\text{a}\space\text{sin}\space\text{θ}}}}$$​ ?

Correct option is C

Given:​

acot θ = b 

cot θ = $$\frac ba$$​​

Solution:

​$$\frac{\text{b}\space\text{cos}\space\text{θ}-{\text{a}\space\text{sin}\space\text{θ}}}{{\text{b}\space\text{cos}\space\text{θ}+{\text{a}\space\text{sin}\space\text{θ}}}}$$

= $$\frac{\frac{bcos\theta }{sin\theta} -a }{\frac{bcos\theta}{sin\theta}+a}$$

=$$\frac{bcot\theta -a }{bcot\theta+a}$$

= $$\frac{b\times \frac ba -a }{b\times \frac ba+a}$$

= $$\frac{\frac{b^2 -a^2}{a}}{\frac{b^2+a^2}{a}}$$ = $$\frac{b^2 -a^2}{b^2+ a^2}$$​​