Question

if if cosθ=x/√x^2-y^2 then prove xsinθ = ycosθ​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: prove : \\ x.sin \: θ = y.cos \: θ \\ \\ given \: that : \\ cos \: θ = \frac{x}{ \sqrt{x {}^{2} + y {}^{2} } } \\ \\ we \: know \: that \\ sin {}^{2} \: θ = 1 - cos {}^{2} θ \\ = 1 - ( \frac{x}{ \sqrt{x {}^{2} + y {}^{2} } } \: ) {}^{2} \\ \\ = 1 - \frac{x {}^{2} }{x {}^{2} + y {}^{2} } \\ \\ = \frac{x {}^{2} + y {}^{2} - x {}^{2} }{x {}^{2} - y {}^{2} } \\ \\ = \frac{y {}^{2} }{x {}^{2} - y {}^{2} } \\ \\ sin \: θ = \frac{y}{ \sqrt{x {}^{2} - y {}^{2} } }$

$thus \: then \: now \: considering \\ x.sin \: θ = y.cos \: θ \\ \\ x \times \frac{y}{ \sqrt{x {}^{2} - y {}^{2} } } = y \times \frac{x}{ \sqrt{x {}^{2} - y {}^{2} } } \\ \\ \frac{xy}{ \sqrt{x {}^{2} - y {}^{2} } } = \frac{xy}{ \sqrt{x {}^{2} - y {}^{2} } } \\ \\ thus \: proved$