Question

prove the Identity,sin0-2sin0/
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2cos0-cos0 = tan0
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Answer 1

Correct Question:-

$\sf{Prove\: the\: identity -> \dfrac{Sin\theta - 2Sin\theta}{2Cos\theta - Cos\theta}= -Tan\theta}$

Solution:-

LHS,

$\sf{\dfrac{Sin\theta - 2Sin\theta}{2Cos\theta - Cos\theta}}$

= $\sf{\dfrac{Sin\theta (1 - 2)}{Cos\theta(2 - 1)}}$

= $\sf{\dfrac{Sin\theta \times -1}{Cos\theta \times 1}}$

= $\sf{\dfrac{-Sin\theta}{Cos\theta}}$

= $\sf{-Tan\theta = RHS (Proved)}$

About Trigonometric Identities:-

• $\sf{Sin\theta = \dfrac{1}{cosec\theta}}$

• $\sf{Cos\theta = \dfrac{1}{Sec\theta}}$

• $\sf{Tan\theta = \dfrac{1}{Cot\theta}}$

• $\sf{\dfrac{Sin\theta}{Cos\theta} = Tan\theta}$

• $\sf{\dfrac{Cos\theta}{Sin\theta} = Cot\theta}$

• $\sf{{Sin}^{2}\theta + {Cos}^{2}\theta = 1}$

• $\sf{1 + {Tan}^{2}\theta = {Sec}^{2}\theta}$

• $\sf{1 + {Cot}^{2}\theta = {Cosec}^{2}\theta}$