Question

please help maths class 11 and spammers will be reported ​

Answer 1

Answer:

(B) cos 7°

Step-by-step explanation:

(sin 47° - sin 25°) + (sin 61° - sin 11°)

= (2cos 36° × sin 11°) + (2cos 36° × sin 25°)

= 2cos 36°(sin 11° + sin 25°)

= 4cos 36° × sin 18° × cos 7°

= 4 × [(√5 + 1)/4] × [(√5 - 1)/4] × cos 7°

= [(√5 + 1)(√5 - 1)]/4 × cos 7°

= [(√5)² - (1)²]/4 × cos 7°

= (5 - 1)/4 × cos 7°

= 4/4 × cos 7°

= cos 7°

Answer 2

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$= ( \sin(47°) - \sin(25°) ) + ( \sin(61°) - \sin(11°) )$

$= (2 \cos(36 \times \sin(11°) ) + 2 \cos(36°) \times \sin(25°)$

$= 2 \cos(36°) ( \sin(11°) + \sin(25°) )$

$= 4 \cos(36°) ( \sin(11°) + \sin(25°) )$

$\sin(18°) = ( \sqrt{5} - 1) \div 4 \: and \:$

$\cos(36°) = ( \sqrt{5} - 1) \div 4$

$therefore$

$answer \: is \: \cos(7°)$