Match the following columns :

Answer

`atos;btos;ctop;dtor`

Explanation

(a) `(99pi)/2ltthetalt50pirArrtheta in` 4thquadrant
`:. Abscostheta=costhetaand abssintheta=-sintheta`
`:. X=-sin^2thetaand y=cos^2theta`
`rArr y-x=1`
(b) `E=((-cosx)(cos^3x)-cosx.sin^3x)/(-cosxsinx-cos^2x)+tanx/sec^2x`
`=(cos^4+cosx+sin^3x)/(sinxcosx+cos^2x)+sinx/secx`
`=(cosx(sin^3x+cos^3x))/(cosx(sinx+cosx))+sinxcosx`
`=(1-sinxcosx)+sinxcosx=1`
(c ) `sin(-870^@)+cosec(-660^@)+tan(-855^@)+2cot(840^@)+cos(480^@)+sec(990^@)`
`=-sin(810^@+60^@)-cosec(720^@-60^@)-tan(810^@+45^@)+2cot120^@+cos120^@+sec180^@`
`=-1/2+2/sqrt3+1-2/sqrt3-1/2-1=-1`
(d) `2((-sin^3x)(cotx)(-secx)(-secx))/(cotxtan^2xsinx)=-2`