Question

prove that:
4 (sin⁴30° + cos⁴ 60°)
- 3 (cos ²45° - sin²90°) = 4.​

Answer 1

To prove - [ RHS has to be 2 and not 4 ]

4 (sin⁴30° + cos⁴ 60°) - 3 (cos ²45° - sin²90°) = 2

Proof -

This can be done by substituting and simplifying .

We know that -

sin 30 = ½

cos 60 = ½

cos 45 = 1/√2

sin 90 = 1 .

Substituting these values , the LHS simplifies to :

=> 4 [ ½ ]⁴ + 4 [½ ]⁴ - 3 [ 1/√2 ]² + 3 [ 1 ]²

=> 4 [ 1/16 ] + 4 [ 1/16 ] - 3 [ ½ ] + 3

=> ¼ + ¼ - 3 [ ½ ] + 3

=> ½ - 3 [1/2] + 3

=> ½ [ 1 - 3 ] + 3

=> 3 - 1

=> 2 .

Hence Proved

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Answer 2

Step-by-step explanation:

Correct Question :

• 4 (sin⁴30° + cos⁴ 60°) - 3 (cos ²45° - sin²90°) = 2

To Prove :

• 4 (sin⁴30° + cos⁴ 60°) - 3 (cos ²45° - sin²90°) = 2

$olution :

4(SIN⁴30 + COS⁴60) - 3(COS²45 - SIN²90)

= 4[(1/2)⁴ + (1/2)⁴] - 3] - 3[(1/√2)² - (1)² ]

= 4[1/16 + 1/16] - 3(1/2 - 1)

= 4 × 2/16 - 3 × (- 1/2)

= 1/2 + 3/2

= 4/2

= 2

Hence Proved !!