If (tan 26° + tan 19°)/(x(1-tan26° tan 19°)) = cos 60°, then the value of x is

Question

If \(\frac{tan\,26°+tan\,19°}{x(1-tan\,26°tan\,19°)}\) = cos 60° then the value of x is

(a) 1 

(b) √2 

(c) 2 

(d) √3

Answer 1

(c) 2

  \(\frac{tan\,26°+tan\,19°}{x(1-tan\,26°tan\,19°)}\) = cos 60°

= \(\frac{tan\,26°+tan\,19°}{1-tan\,26°tan\,19°}\) = x cos 60°

= tan (26° + 19°) = \(x\) x \(\frac12\) \(\bigg[∵ tan (A + B)=\frac{tan\,A+tan\,B}{1-tan\,A\,tan\,B}\bigg]\)

= tan 45° = \(\frac{x}{2}\) ⇒ \(\frac{x}{2}\) = 1 ⇒ x = 2.