Question

tan theta = 4/3 find sin×2 theta + cos × 2 theta = ?​

Answer 1

Given:—

$† \: \: \: \: tan \theta \: = \frac{4}{3}$

${\implies \: \frac{sin \theta}{cos \theta} = \frac{4}{3} }$

$\implies \: \underline\bold{sin \theta \: = 4} \: \: \: \: \: and \: \: \: \: \: \underline\bold{cos \theta = 3}$

Now ,

$sin2 \theta \: + \: cos2 \theta$

$= 2( \sin \theta \: + cos \theta) + {cos}^{2} \theta - {sin}^{2} \theta$

$= 2(4 + 3) + ( {3)}^{2} - ({4)}^{2}$

$= 2 \times 7 + {9} - 16$

$= 14 - 7$

$= \bold7$