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Question Number 143913 by Sravanth last updated on 19/Jun/21

If ((cos α)/(cos β)) = m and ((cos α)/(sin β)) = n then prove that (m^2 +n^2 )cos^2 β = n^2

$$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$

Answered by Ar Brandon last updated on 19/Jun/21

cos^2 β+sin^2 β=1 (((cosα)/m))^2 +(((cosα)/n))^2 =1 (((n^2 +m^2 )cos^2 α)/(m^2 n^2 ))=1 (((m^2 +n^2 ))/(m^2 n^2 ))∙((m^2 cos^2 β)/1)=1 (m^2 +n^2 )cos^2 β=n^2

$$\mathrm{cos}^{\mathrm{2}} \beta+\mathrm{sin}^{\mathrm{2}} \beta=\mathrm{1} \\ $$$$\left(\frac{\mathrm{cos}\alpha}{\mathrm{m}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{cos}\alpha}{\mathrm{n}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$$\frac{\left(\mathrm{n}^{\mathrm{2}} +\mathrm{m}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \alpha}{\mathrm{m}^{\mathrm{2}} \mathrm{n}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)}{\mathrm{m}^{\mathrm{2}} \mathrm{n}^{\mathrm{2}} }\centerdot\frac{\mathrm{m}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \beta}{\mathrm{1}}=\mathrm{1} \\ $$$$\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta=\mathrm{n}^{\mathrm{2}} \\ $$

Commented by Dwaipayan Shikari last updated on 19/Jun/21

I know who is AIR BRANDON but i don′t who is AR BRANDON. Then Congratulations too! It your first post (answer)

$${I}\:{know}\:{who}\:{is}\:{AIR}\:{BRANDON}\:{but}\:{i}\:{don}'{t}\: \\ $$$${who}\:{is}\:{AR}\:{BRANDON}.\:{Then}\:{Congratulations}\: \\ $$$${too}!\:{It}\:{your}\:{first}\:{post}\:\left({answer}\right) \\ $$

Commented by Dwaipayan Shikari last updated on 19/Jun/21

I pronouce AR Brandon as Air Brandon

$${I}\:{pronouce}\:{AR}\:{Brandon}\:{as}\:{Air}\:{Brandon} \\ $$

Commented by Ar Brandon last updated on 19/Jun/21

Hahaha ! accepted. AR →Arung Ar Brandon→Arung Brandon 😉

$$\mathrm{Hahaha}\:!\:\mathrm{accepted}. \\ $$$$\mathrm{AR}\:\rightarrow\mathrm{Arung}\: \\ $$$$\mathrm{Ar}\:\mathrm{Brandon}\rightarrow\mathrm{Arung}\:\mathrm{Brandon} \\ $$😉

Commented by Dwaipayan Shikari last updated on 19/Jun/21

What does Arung mean?

$${What}\:{does}\:\:{Arung}\:{mean}? \\ $$

Commented by Ar Brandon last updated on 19/Jun/21

It's my name ����������

Commented by Dwaipayan Shikari last updated on 19/Jun/21

Yes but it must have a meaning Like Dwaipayan means “A man who was born in an Island” and the writer of Indian Epic Mahab^− harata

$${Yes}\:{but}\:{it}\:{must}\:{have}\:{a}\:{meaning} \\ $$$${Like}\:{Dwaipayan}\:{means}\:``{A}\:{man}\:{who} \\ $$$${was}\:{born}\:{in}\:{an}\:{Island}''\:{and}\:{the}\:{writer} \\ $$$${of}\:{Indian}\:{Epic}\:{Maha}\overset{−} {{b}harata} \\ $$

Commented by Sravanth last updated on 19/Jun/21

Thanks Bro

Commented by Ar Brandon last updated on 19/Jun/21

It's a pleasure answering your first post. Welcome to forum Sravanth ! ��

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