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L.H.S.
= 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 {(1 + 6)/2} - 6 {(3 - 2)/6}
= 7 - 1
= 6
= R.H.S.
Hence, proved.
= 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 {(1 + 6)/2} - 6 {(3 - 2)/6}
= 7 - 1
= 6
= R.H.S.
Hence, proved.
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