$sin 47^{\circ} + sin 61^{\circ} - sin 11^{\circ} - sin 25^{\circ}$ is equal to

sin 36^{\circ}

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cos 36^{\circ}

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sin 7^{\circ}

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cos 7^{\circ}

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Solution

The correct option is B $cos 7^{\circ}$
The given expression is equal to
$(sin 47^{\circ} + sin 61^{\circ}) - (sin 11^{\circ} + sin 25^{\circ})$

$= 2 sin 54^{\circ} cos 7^{\circ} - 2 sin 18^{\circ} cos 7^{\circ}$

$= 2 cos 7^{\circ} (sin 54^{\circ} - sin 18^{\circ})$

$= 2 cos 7^{\circ} [\frac{\sqrt{5} + 1}{4} - \frac{\sqrt{5} - 1}{4}] = cos 7^{\circ}$ .

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Similar questions

Q. sin 47° + sin 61° − sin 11° − sin 25° is equal to
(a) sin 36°
(b) cos 36°
(c) sin 7°
(d) cos 7°

$s i n 47^{\circ} + s i n 61^{\circ} - s i n 11^{\circ} - s i n 25^{\circ}$ is equal to

Q. The value of

x \in (0, 90^{\circ})

satisfying

c o s x = s i n 61^{\circ} + s i n 47^{\circ} - s i n 25^{\circ} - s i n 11^{\circ}

, where

sin 18^{\circ} = \frac{\sqrt{5} - 1}{4}

$cos 36^{\circ} = \frac{\sqrt{5} + 1}{4}$

Q. Find the value of

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

Evaluate the following:
(i) $s i n 78^{\circ} c o s 18^{\circ} - c o s 78^{\circ} s i n 18^{\circ}$
(ii) $c o s 47^{\circ} c o s 13^{\circ} - s i n 47^{\circ} s i n 13^{\circ}$
(iii) $s i n 36^{\circ} c o s 9^{\circ} + c o s 36^{\circ} s i n 9^{\circ}$
(iv) $c o s 80^{\circ} c o s 20^{\circ} + s i n 18^{\circ} s i n 20^{\circ}$

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sin47∘+sin61∘−sin11∘−sin25∘ is equal to

The correct option is B cos7∘The given expression is equal to(sin47∘+sin61∘)−(sin11∘+sin25∘)=2sin54∘cos7∘−2sin18∘cos7∘=2cos7∘(sin54∘−sin18∘)=2cos7∘[√5+14−√5−14]=cos7∘.

$sin 47^{\circ} + sin 61^{\circ} - sin 11^{\circ} - sin 25^{\circ}$ is equal to