prove that 2 (cos² 45 + tan² 60) - 6 (sin² 45 + tan² 30) = 6

2[(1/21/2)2+(31/2)2 ]  -  6[(1/21/2)2 + (1/31/2)2
=2[1/2+3] - 6[1/2+1/3]
= 2[7/2] -  6[5/6]
= 7 - 5
=2
which is not equal plz recheck ur question.
 
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Please recheck your question.
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LHS 2(cos²45° + tan²60°) - 6(sin²45° - tan²30°) =2[(1/√2)² + (√3)²] - 6[(1/√2)² - (1/√3)²] =2{[(1/2)+3] - 6[(1/2)-(1/3)]} =2(7/2) - 6(3-2/6) =7-1 =6 RHS 6 By comparing we get LHS = RHS HENCE PROVED ✓
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