Question

2. Hallar el valor de “x”: tg 5x = cotg x


3. Hallar el valor de “x”: cos 3x - sen 45° = 0


4. Si sec (2x – 30°) = cosec (3x + 20°), hallar el valor de “x”

Answer 1

2) 
       $\tan 5x=\cot x\\ \tan 5x=\tan [90\cdot (2k-1)-x]\; ,\; k \in\mathbb Z\\ 5x=90\cdot (2k-1)-x\\ \boxed{x=15(2k-1)}$

3)
      $\cos 3x = \sin 45\\ \cos 3x = \cos 45\\ \cos 3x = \cos(45+360 k)\;,\; k\in \mathbb Z\\ 3x=45+360 k\\ \\ \boxed{x=15+120k}$

4)
     
           $\sec (2x-30)=\csc(3x+20)\\ \sec (2x-30)=\sec[3x+20+270(2k+1)]\;,\; k\in \mathbb Z\\ 2x-30=3x+20+270(2k+1)\\ \\ \boxed{x=-50-270(2k+1)}$