Prove that the value of (sin^(3) (2pi - theta))/(cos^2 ((3pi)/2 + theta)) cdot (cos^3(2pi - theta))/(sin^3(2pi + theta)) cdot (tan(pi - theta))/("cosec"^2(pi - theta)) cdot ("sec"^2(pi + theta))/(sin theta) . Is independent of theta .
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Step-by-step explanation:
= -sin3theta/sin2theta .cos3theta/sin3theta .-tantheta/cosec2theta .(-sectheta)2/sintheta
= -sin3theta/sin2theta .cos3theta/sin3theta .-tantheta/cosec2theta .secwtheta/sintheta
= -1 .1/sec3theta . sec2theta .cosec3theta .1/cosec2theta .-tantheta
= -1 .costheta/sintheta . -tantheta
= -1 .1/tantheta . -tantheta
= 1(ans)
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