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If (cos A)/(cos B)=p,(sin A)/(sin B)=q, ...

If `(cos A)/(cos B)=p`,`(sin A)/(sin B)=q`, then `(p^2(q^2-1))/(p^2-q^2)` is equal to (A) `-cos^2 A` (B) `cos^2 B` (C) `cos^2 A` (D)`sin^2 B`

Text Solution

Verified by Experts

`p = cosA/cosB` , `q = sinA/sinB`
`:. q^2-1 = sin^2A/sin^2B - 1 = (sin^2A-sin^2B)/sin^2B`
`(p^2-q^2) = cos^2A/cos^2B - sin^2A/sin^2B`
`=(sin^2Bcos^2A-sin^2Acos^2B)/(sin^2Bcos^2B)`
`=((1-sin^2A)sin^2B -sin^2A(1-sin^2B))/(sin^2Bcos^2B)`
`=(sin^2B-sin^2A)/(sin^2Bcos^2B)`
`=-((q^2-1))/(cos^2B)`
`:. (q^2-1)/(p^2-q^2) = -cos^2B`
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