question_answer

If\[4\sin \theta =3\cos \theta \],find\[\frac{{{\sec }^{2}}\theta }{4(1-{{\tan }^{2}}\theta )}\].

A)  \[\frac{25}{16}\]                             

B)         \[\frac{25}{28}\]

C)  \[\frac{1}{4}\]                  

D)         \[\frac{5}{6}\]

Correct Answer: B

Solution :

                            \[=(\text{25}\times \text{7})\text{(2}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{3}}}\text{) c}{{\text{m}}^{\text{2}}}\] \[={{\text{2}}^{\text{6}}}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{4}}}\text{c}{{\text{m}}^{\text{2}}}\] \[2-\sqrt{4}=2-2=0\]       \[{{(\sqrt{5})}^{2}}=5\] \[\sqrt{9}-\sqrt{4}=3-2=1\] \[\sqrt{2}-\sqrt{3}\]        \[1789=29x+49\] \['x'\]