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प्रश्न
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
उत्तर
LHS = `4(sin^4 30°+ cos^4 60°)- 3(cos^2 45° – sin^2 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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