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If x=asinthetaa n dy=btantheta, then pro...

If `x=asinthetaa n dy=btantheta,` then prove that `(a^2)/(x^2)-(b^2)/(y^2)=1`

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We have
` x= a sin theta rArr (a)/(x)=(1)/(sin theta) rArr (a)/(x) = "cosec" theta " "...(i) `
` and y= b tan theta rArr (b)/(y)= (1)/(tan theta) rArr (b)/(y) = cot theta. " "...(ii) `
Squaring (i) and (ii) and subtracting, we get
`((a^(2))/(x^(2))- (b^(2))/(y^(2)))= ( "cosec"^(2)theta - cot^(2)theta ) =1. `
Hence, ` ((a^(2))/(x^(2))- (b^(2))/(y^(2)))=1. `
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Test Yourself
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  5. If sin theta=(sqrt(3))/(2)" then " ("cosec"theta+cot theta)=?

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  7. If 2x=secA and (2)/(x)=tanA, " prove that " (x^(2)-(1)/(x^(2)))=(1)/(4...

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  11. Prove that sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).

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  13. Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

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  14. If 5cottheta=3. find the value of (5sintheta-3costheta)/(4sintheta+3co...

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