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If tan(x +y) = 3/4 and tan (x - y) = 8/15. prove that tan2x = 77/36

written 5.6 years ago by teamques10 ★ 69k

modified 3.0 years ago by pedsangini276 • 4.8k

engineering mathematics

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written 5.6 years ago by teamques10 ★ 69k

Solution:

Consider

$$\begin{aligned} 2 x=& x+y+x-y \ \tan 2 x &=\tan (x+y+x-y) \ &=\frac{\tan (x+y)+\tan (x-y)}{1-\tan (x+y) \tan (x-y)} \ &=\frac{\frac{3}{4}+\frac{8}{15}}{1-\frac{3}{4} \frac{8}{15}} \ &=\frac{77}{36} \ \therefore \tan 2 x &=77 / 36 \end{aligned}$$

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