Q28 of 123 Page 9

If and x lies in the IIIrd quadrant, find the values of and sin 2x.

Given:




We know,


cos 2x = 2 cos2 x – 1









Since,




So,



We know,


cos 2x = 1 – 2 sin2 x









Since,




So,



We know,


sin2 x + cos2 x = 1


⇒ sin2 x = 1 – cos2 x








Since,




So,



Now,


sin 2x = 2(sin x)(cos x)






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