Question

Question 4 (iv)
Choose the correct option. Justify your choice.
(iv) $\frac{1+ta{n}^{2}A}{1+co{t}^{2}A}$
(A) $se{c}^{2}A$
(B) -1
(C) $co{t}^{2}A$
(D) $ta{n}^{2}A$

Answer 1

(iv) (D) is correct.
$\frac{1+ta{n}^{2}A}{1+co{t}^{2}A}=\frac{(1+\frac{si{n}^{2}A}{co{s}^{2}A})}{(1+\frac{co{s}^{2}A}{si{n}^{2}A})}=\frac{\left(\frac{co{s}^{2}A+si{n}^{2}A}{co{s}^{2}A}\right)}{\left(\frac{si{n}^{2}A+co{s}^{2}A}{si{n}^{2}A}\right)}=\frac{\left(\frac{1}{co{s}^{2}A}\right)}{\left(\frac{1}{si{n}^{2}A}\right)}=\left(\frac{si{n}^{2}A}{co{s}^{2}A}\right)=ta{n}^{2}A$