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1. Eliminate θ from the given equations, x = a cot θ – b cosec θ y = a cot θ + b cosec θ Solution: x = a cot θ – b cosec θ …(I) y = a cot θ + b cosec θ …(II) Adding equations (I) and (II), x + y = ∴ cot θ = + Subtracting equation (I) from (II), y – x = ∴ cosec θ = Now, cosec2 θ – cot2 θ = 1 …(Identity) ∴ ( − ) − = 1 ∴ (−) − (+) = 1 ∴ ( − ) − ( ∗ ) = |
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Answer» ANSWERWe have,x=a(cscθ+cotθ) ……. (1)y=b(cscθ−cotθ) …….. (2) From EQUATION (1) and (2), we getxy=ab(cscθ+cotθ)(cscθ−cotθ)xy=ab(csc2θ−cot2θ)xy=ab[∵csc2x−cot2x=1] HENCE, this is the ANSWER. |
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