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Fittoniya [83]
2 years ago
5

Tan2A - sin2A =sin2Atan2A​

Mathematics
1 answer:
Kitty [74]2 years ago
4 0

Step-by-step explanation:

\tan^2\alpha-\sin^2\alpha=\sin^2\alpha\tan^2\alpha\\\\LS=\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2-\sin^2\alpha=\dfrac{\sin^2\alpha}{\cos^2\alpha}-\dfrac{\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}\\\\=\dfrac{\sin^2\alpha-\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}=\dfrac{\sin^2\alpha(1-\cos^2\alpha)}{\cos^2\alpha}=\dfrac{\sin^2\alpha\sin^2\alpha}{\cos^2\alpha}\\\\=\sin^2\alpha\cdot\dfrac{\sin^2\alpha}{\cos^2\alpha}=\sin^2\alpha\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2=\sin^2\alpha\tan^2\alpha=RS

Used:

\tan x=\dfrac{\sin x}{\cos x}\\\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\sin^2\alpha+\cos^2\alpha=1\to \sin^2\alpha=1-\cos^2\alpha\\\\\text{distributive property}\ a(b+c)=ab+ac

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