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Prove that: 4 (sin^4 30° + cos^4 60°) – 3 (cos^2 45° – sin^2 90°) = 2 - Mathematics

Question

Prove that:

4 (sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°) = 2

Theorem

Solution

LHS = 4 (sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°)

= `4[(1/2)^4 + (1/2)^4] - 3[(1/sqrt2)^2 + (1)^4]`

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

= `(4 xx 2)/(16) + 3 xx (1)/(2)`

= 2

RHS = 2

LHS = RHS

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Q 6.2 Q 6.1 Q 7.1

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] - Exercise 23 (A) [Page 291]

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Selina Concise Mathematics [English] Class 9 ICSE

Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 6.2 | Page 291

Nootan Mathematics [English] Class 9 ICSE

Chapter 18 Trigonometric Ratios of Some Standard Angles and Complementary Angles
Exercise 18A | Q 16. (ii) | Page 373