India Languages, asked by tvlu7103, 9 months ago

cosα/cosβ=m மற்றும் cosα/cosβ=n கொண்டு (m^2+n^2 ) cos^2 β=n^2 என்பதை நிருபி

Answers

Answered by steffiaspinno
0

விளக்கம்:

\frac{\cos \alpha}{\cos \beta}=\mathrm{m}

\frac{\cos \alpha}{\cos \beta}=n

நிரூபிக்க வேண்டியவை

\left(m^{2}+n^{2}\right) \cos ^{2} \beta=n^{2}

=\left[\left[\frac{\cos \alpha}{\cos \beta}\right]^{2}+\left[\frac{\cos \alpha}{\cos \beta}\right]^{2}\right] \cos ^{2} \beta

\left[\frac{\cos ^{2} \alpha}{\cos ^{2} \beta}+\frac{\cos ^{2} \alpha}{\sin ^{2} \beta}\right] \cos ^{2} \beta

\left[\frac{\sin ^{2} \beta \cos ^{2} \alpha+\cos ^{2} \beta \cos ^{2} \alpha}{\cos ^{2} \beta \sin ^{2} \beta}\right] \cos ^{2} \beta

\frac{\sin ^{2} \beta \cos ^{2} a}{\sin ^{2} \beta}+\frac{\cos ^{2} \beta \cos ^{2} \alpha}{\sin ^{2} \beta}

=\cos ^{2} \alpha+\frac{\cos ^{2} \beta\left(1-\sin ^{2} \beta\right)}{\sin ^{2} \beta}

= \cos ^{2} \alpha+\frac{\cos ^{2} \beta}{\sin ^{2} \beta}-\frac{\sin ^{2} \beta \cos ^{2} \alpha}{\sin ^{2} \beta}

\Rightarrow \cos ^{2} \alpha+\frac{\cos ^{2} \alpha}{\sin ^{2} \beta}-\cos ^{2} \alpha

\Rightarrow \frac{\cos ^{2} a}{\sin ^{2} \beta}=\left(\frac{\cos \alpha}{\sin \beta}\right)^{2}=n^{2} = வலப்பக்கம்

\frac{\cos \alpha}{\cos \beta}=\mathrm{m} மற்றும் \Rightarrow \frac{\cos ^{2} a}{\sin ^{2} \beta}=\left(\frac{\cos \alpha}{\sin \beta}\right)^{2}=n^{2}  எனில்

\left(m^{2}+n^{2}\right) \cos ^{2} \beta=n^{2}  என நிருபிக்கபட்டது.

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