Evaluate the following-i sin 78-cos 18-cos 78-sin 18-ii cos 47-cos 13-sin 47-sin 13-iii sin 36-cos 9-cos 36-sin 9-iv cos 80-cos 20-sin 18-sin 20-

(i) sin 78^∘cos18^∘ cos78^∘ sin18^∘ [sin(A B)=sinA cosB cosAsinB] = sin(78^∘ 18^∘) = sin60^∘ = √(3)/2 (ii) cos47^∘ cos13^∘ sin47^∘sin13^∘ [cos(A+B)=sinAcosB+c ...

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Byju's Answer

Standard XII

Mathematics

Cos(A+B)Cos(A-B)

Evaluate the ...

Question

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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Solution

(i) $s i n 78^{\circ} c o s 18^{\circ} - c o s 78^{\circ} s i n 18^{\circ}$
$[s i n (A - B) = s i n A c o s B - c o s A s i n B]$
$= s i n (78^{\circ} - 18^{\circ})$
$= s i n 60^{\circ}$
$= \frac{\sqrt{3}}{2}$

(ii) $c o s 47^{\circ} c o s 13^{\circ} - s i n 47^{\circ} s i n 13^{\circ}$
$[c o s (A + B) = s i n A c o s B + c o s A s i n B]$
$= s i n (47^{\circ} + 13^{\circ})$
$= c o s 60^{\circ}$
$= \frac{1}{2}$

(iii) $s i n 36^{\circ} c o s 9^{\circ} + c o s 36^{\circ} s i n 9^{\circ}$
$[s i n (A + B) = s i n A c o s B + c o s A s i n B]$
$= s i n (36^{\circ} + 9^{\circ})$
$= s i n 45^{\circ}$
$= \frac{1}{\sqrt{2}}$

(iv) $c o s 80^{\circ} c o s 20^{\circ} + s i n 18^{\circ} s i n 20^{\circ}$
$[c o s (A - B) = c o s A c o s B + s i n A s i n B]$
$= s i n (80^{\circ} - 20^{\circ})$
$= c o s 60^{\circ}$
= $\frac{1}{2}$

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Q. The value of

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, where

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Evaluate the following: (i) sin78∘cos18∘−cos78∘sin18∘ (ii) cos47∘cos13∘−sin47∘sin13∘ (iii) sin36∘cos9∘+cos36∘sin9∘ (iv) cos80∘cos20∘+sin18∘sin20∘