Question

tan^2pi/16+tan^22pi/16​

Answer 1

$\underline{\underline{\bf \purple{Correct\; Question :-}}}$

$\sf tan^2\bigg(\dfrac{\pi}{16}\bigg) + tan^2\bigg(\dfrac{2\pi}{16}\bigg)$

$\underline{\underline{\bf \green{Solution:-}}}$

$\rm Substituting\;\boxed{\red{\pi = 180^\circ}}\\\\\longrightarrow \sf tan^2\bigg(\dfrac{180}{16}\bigg)+tan^2\bigg[\dfrac{2(180)}{16}\bigg] \\\\\sf \longrightarrow tan^2(11.25^\circ) + tan^2\bigg(\dfrac{360}{16}\bigg) \\\\\sf\longrightarrow tan^2(11.25^\circ) + tan^2(22.5^\circ) \\\\\sf\longrightarrow (0.19)^2 + (0.41)^2 \\\\\longrightarrow \sf 0.0361 + 0.1681 \\\\\dagger \underline{\boxed{\bf 0.2042}}$

$\underline{\underline{\bf \orange{More \; information :}}}$

$\boxed{\begin{minipage}{6.6cm}\bf\underline{Important trigonometric identities :-}\\\\\sf\underline{Identity 1 :}\;sin^2\theta+cos^2\theta=1\\\\\sf\underline{Identity 2:}\;sec^2\theta-tan^2\theta=1\\\\\sf\underline{Identity 2:}\;cosec^2\theta-tan^2\theta\end{minipage}}$