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Prove that (i)sin(40^(@)-theta)cos(...

Prove that
(i)`sin(40^(@)-theta)cos(50^(@)+theta)=0`
(ii) `1sec(65^(@)+theta)-"cesec"(25^(@)-theta)=0`

Text Solution

Verified by Experts

(i) L.H.S. `=sin(40^(@)-theta)-cos(50^(@)+theta)-cos(50^(@)+theta)`
`=sin{90^(@)-(50^(@)+theta)}-cos(50^(@)+theta)`
`=cos(50^(@)+theta)-cos(50^(@)+theta)=0=R.H.S.`
(ii) L.H.S.`=sec(65^(@)+theta)-"cosec"(25^(@)-theta)`
`=sec{90^(@)-(25^(@)-theta)}-"cosec"(25^(@)-theta)`
`="cosec"(25^(@)-theta)-"cosec"(25^(@)-theta)=0=R.H.S.`
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