Question

Pls help me out...............
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Answer 1

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→$\frac{Sin\theta - 2Sin^3\theta}{2Cos^3\theta-Cos\theta}=Tan\theta$

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⇒$\frac{Sin\theta - 2Sin^3\theta}{2Cos^3\theta-Cos\theta}$

⇒$\frac{Sin\theta (1- 2Sin^2\theta )}{Cos\theta (2Cos^2\theta - 1)}$

⇒$\frac{Sin\theta \big( 1-2(1-Cos^2\theta ) \big) }{Cos\theta (2Cos^2\theta -1)}$

⇒$\frac{Sin\theta ( 1-2+2Cos^2\theta ) }{Cos\theta (-1+2Cos^2\theta )}$

⇒$\frac{Sin\theta {\cancel{(2Cos^2\theta -1)}}}{Cos\theta {\cancel{(2Cos^2\theta -1)}}}$

⇒$\Large{\frac{Sin\theta }{Cos\theta }}$

⇒$\huge{\pink{\overbrace{\underbrace{Tan\theta}}}}$

⭐Hence Proved⭐

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Formulas Used :-

• $Sin^2\theta = 1-Cos^2\theta$
• $Cos^2\theta = 1-Sin^2\theta$

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