If $tan\frac{\theta}{2} = \frac{2}{3} find the value of 2sin\theta + 3sin\theta.$

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written 5.2 years ago by

teamques10 ★ 68k

modified 2.6 years ago by

pedsangini276 • 4.8k

engineering mathematics

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written 5.2 years ago by

teamques10 ★ 68k

Solution: $2 \sin \theta+3 \cos \theta =2\left(\frac{2 \tan \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}\right)+3\left(\frac{1-\tan ^{2} \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}\right)$

$=2\left(\frac{2 \times \frac{2}{3}}{1+\left(\frac{2}{3}\right)^{2}}\right)+3\left(\frac{1-\left(\frac{2}{3}\right)^{2}}{1+\left(\frac{2}{3}\right)^{2}}\right) =3$

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