22.2sin2_+ cosec

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Solution

Simplifying the L.H.S,

2 sin 2 π 6 + cosec 2 7π 6 ⋅ cos 2 π 3 =2 ( 1 2 ) 2 + cosec 2 ( π+ π 6 ) ( 1 2 ) 2 =2× 1 4 +( - cosec 2 π 6 ) ( 1 2 ) 2 = 1 2 + ( −2 ) 2 ( 1 4 ) = 1 2 +1 = 3 2 =R.H.S

L.H.S. = R.H.S.

Hence, proved.

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