Trigonometry! #44

Geometry Level 3

True or false?

If tan ⁡ A = 1 − cos ⁡ B sin ⁡ B \tan A = \frac{1-\cos B}{\sin B} then tan ⁡ 2 A = tan ⁡ B \tan 2A = \tan B

This problem is part of the set Trigonometry .

Can't say False Sometimes true, sometimes false True

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Omkar Kulkarni by Omkar Kulkarni , 22, India

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2 solutions

Omkar Kulkarni
Feb 14, 2015

tan ⁡ A = 1 − cos ⁡ B sin ⁡ B = 2 sin ⁡ 2 B 2 2 sin ⁡ B 2 cos ⁡ B 2 tan ⁡ A = tan ⁡ B 2 ∴ tan ⁡ 2 A = tan ⁡ B \large{\tan A = \frac{1-\cos B}{\sin B} \\ = \frac{2\sin^{2}\frac{B}{2}}{2\sin\frac{B}{2}\cos\frac{B}{2}} \\ \tan A = \tan \frac{B}{2} \\ \therefore \tan 2A = \tan B}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Jerome Polin
Feb 1, 2015

Tan A = (1-cos2A) / (sin 2A) , 2A=B. Hence, tan 2A=tanB

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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