Find the value of x, if x = (Tan^{2}30° + Cosec^{2}45° + Sin^{2}90°)/(1 + Sin^{2}45° + Sec^{2}30°).

Option 2 : 20/17

**Given:**

x = (Tan230° + Cosec245° + Sin290°)/(1 + Sin245° + Sec230°)

**Concept used:**

**Calculation:**

According to question, we have

x = (Tan^{2}30° + Cosec^{2}45° + Sin^{2}90°)/(1 + Sin^{2}45° + Sec^{2}30°)

⇒ x = \(\left( {\frac{{\frac{1}{3}\; + \;2\; + \;1\;\;}}{{1\; + \;\frac{1}{2}\; + \;\frac{4}{3}}}} \right)\)

⇒ x = \(\left( {\frac{{\frac{{1\; + \;6\; + \;3}}{3}\;}}{{\frac{{6\; + \;3\; + \;8\;}}{6}}}} \right)\)

⇒ x = \(\left( {\frac{{\frac{{10}}{3}\;}}{{\frac{{17\;}}{6}}}} \right)\)

⇒ x = (10/3) × (6/17)

⇒ x = 20/17

**∴**** The value of x is 20/17.**