Answer :

(i)

Cos840° = Cos(2.360° + 120°) …………(using Cos(2ϖ + x) = Cosx)


= Cos(120°)


= Cos(180° - 60°)


= - Cos60° ……………(using Cos(ϖ - x) = - Cosx)



(ii) sin870° = sin(2.360° + 150°) ………….(using sin(2ϖ + x) = sinx)


= sin150°


= sin(180° - 30°) ………(using sin(ϖ - x) = sinx)


= sin30°



(iii)tan( - 120°) = - tan12 …….(tan( - x) = tanx)


= - tan(180° - 60°) ……. (in II quadrant tanx is negative)


= - ( - tan60°)


= tan60°



(iv)


= ………..(using cos( - x) = - cosx)


= ………...(using cos(2ϖ + x) = cosx)


=


(v)


……..(IV quadrant sinx is negative)



(vi)tan225° = tan(180° + 45°) …………(in III quadrant tanx is positive)



(vii)


.….(tan( - x) = - tanx)


…..(in IV quadrant tanx is negative)


(viii)sin( - 1230°) = sin1230° ………….(using sin( - x) = sinx)


= sin(3.360° + 150°)


= sin150°


= sin(180° - 30°) ………….(using sin(180° - x) = sinx)


= sin30°



(ix)cos495° = cos(360° + 135°) …………(using cos(360° + x) = cosx)


= cos135°


= cos(180° - 45°) ………….(using cos(180° - x) = - cosx)


= - cos45°



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