Evaluate: cos51∘ sin39∘ +2tan11∘ tan31∘ tan45∘ tan59∘ tan79∘ −3(sin221∘ +sin269∘ ) .

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Evaluate: { { 39 }^{ } }{ { 51 }^{ } } +2 { { 11 }^{ }

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Evaluate: $\frac{sin 39 ^{\circ}}{cos 51 ^{\circ}} + 2 tan 11^{\circ} tan 31^{\circ} tan 45^{\circ} tan 59^{\circ} tan 79^{\circ} - 3 (sin^{2} 21^{\circ} + sin^{2} 69^{\circ})$ .

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Evaluate:

\frac{sin 39 ^{\circ}}{cos 51 ^{\circ}} + 2 tan 11^{\circ} tan 31^{\circ} tan 45^{\circ} tan 59^{\circ} tan 79^{\circ} - 3 (sin^{2} 21^{\circ} + sin^{2} 69^{\circ})

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sin 3 9^{o} = sin (90 - 51)^{o} = cos 5 1^{o}

sin 2 1^{o} = sin (90 - 69)^{o} = cos 6 9^{o}

tan 1 1^{o} = tan (90 - 79)^{o} = cot 7 9^{o}

tan 3 1^{o} = tan (90 - 59)^{o} = cot 5 9^{o}

So,

\frac{sin 3 9 ^{o}}{cos 5 1 ^{o}} + 2 tan 1 1^{o} . tan 3 1^{o} . tan 4 5^{o} . tan 5 9^{o} . tan 7 9^{o} - 2 (sin^{2} 2 1^{o} + sin^{2} 6 9^{o})

= \frac{cos 5 1 ^{o}}{cos 5 1 ^{o}} + 2 cot 7 9^{o} . cot 5 9^{o} . tan 4 5^{o} . tan 5 9^{o} . tan 7 9^{o} - 3 (cos^{2} 69 + sin^{2} 6 9^{o})

= 1 + 2 (tan 7 9^{o} . cot 7 9^{o}) (tan 5 9^{o} . cot 5 9^{o}) . tan 4 5^{o} - 3 (1)

= 1 + 2 (1) (1) (1) - 3

= 3 - 3

= 0

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Question Text	Evaluate: $\frac{sin 39 ^{\circ}}{cos 51 ^{\circ}} + 2 tan 11^{\circ} tan 31^{\circ} tan 45^{\circ} tan 59^{\circ} tan 79^{\circ} - 3 (sin^{2} 21^{\circ} + sin^{2} 69^{\circ})$ .
Answer Type	Text solution:1
Upvotes	150