Question

2 (cos square 45 degree + tan square 60 degree) - 6 (sin square 45 degree - tan square 30 degree) = 6

Answer 1

I hope it will help you

Answer 2

Solution :

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We know the values of ,

i) cos 45° = 1/√2

ii) tan 60° = √3

iii ) sin45° = 1/√3

iv) tan 30° = 1/√3

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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 + 3/1] - 6[1/2 - 1/3]

= 2[ (1+6)/2 ] - 6[(3-2)/6]

= 2(7/2) - 6(1/6)

= 7 - 1

= 6

= RHS

Therefore,

2(cos²45°+tan²60°)-6(sin²45°-tan²30°) = 6

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