Question

if sin theta = cos theta find the value of 3tan ^2theta +2 sin^2theta+cos^2 theta​

Answer 1

$\large \sf \maltese \: \: \: \underline{ \underline{Question \: : }}$

• If sin theta = cos theta find the value of 3tan ^2theta +2 sin^2theta+cos^2 theta

$\large \sf \maltese \: \: \: \underline{ \underline{Solution\: : }}$

• From the given sin theta = cos theta ; => tan theta = 1

$\bull \: \: \bf \: 3 \: {\tan}^{2} + 2 \: { \sin}^{2} \theta + { \cos}^{2} \theta \\ \\ \\ : \implies \sf 3 + { \sin}^{2} \theta \: \: \: \: \: \: \bigg[ \bf\because \: \: { \sin}^{2} \theta + { \cos}^{2} \theta = 1 \bigg ] \\ \\ \\ : \implies \sf 3 + 1 - { \cos}^{2} \theta \\ \\ \\ : \implies \sf 4 - \frac{1}{{ \sec}^{2} \theta} \\ \\ \\ : \implies \sf 4 - \frac{1}{1 + { \tan}^{2} \theta } \: \: \: \: \bigg[ \bf \because \: \: \: { \sec}^{2} \theta - { \tan}^{2} \theta = 1] \\ \\ \\ : \implies \sf \: 4 - \frac{1}{1 + 1} \: \: \: \: \: \bigg[ \because \: \bf \: \: \tan \theta = 1 \bigg] \\ \\ \\ \: \large \: \: \therefore \: \: \: { \underline{\boxed{\bf \: \frac{7}{2} \: } \: \: }}_{\bigstar \star}$