If sin (A + B) = sin A cos B + cos A sin B and cos (A - B) = cos A cos B + sin A sin B, find the values of (i) sin $75^{\circ}$ and (ii) cos $15^{\circ} .$

Open in App

Solution

(i) Given $S i n (A + B) = S i n A C o s B + C o s A S i n B$ .

$S i n 75 = S i n (45 + 30) = S i n 45 C o s 30 + C o s 45 S i n 30$ .

$S i n 75 = (\frac{1}{\sqrt{2}}) (\frac{\sqrt{3}}{2}) + (\frac{1}{\sqrt{2}}) (\frac{1}{2}) = \frac{[\sqrt{3} + 1]}{2 \sqrt{2}}$ .

(ii) given $c o s (A - B) = c o s A c o s B + s i n A s i n B$

$c o s 15 ° = c o s (45 - 30) = c o s 45 c o s 30 + s i n 45 s i n 30$

$= (\frac{1}{\sqrt{2}}) (\frac{\sqrt{3}}{2}) + (\frac{1}{\sqrt{2}}) (\frac{1}{2})$

$= \frac{\sqrt{3}}{2 \sqrt{2}} + \frac{1}{2 \sqrt{2}} = \frac{(\sqrt{3} + 1)}{2 \sqrt{2}}$

Suggest Corrections

Similar questions

A = 30^{\circ}

B = 60^{\circ}

sin (A + B) = sin A cos B + cos A sin B

cos (A + B) = cos A cos B - sin A sin B

If sin(A - B) = sinA cos B - cosA sinB and cos(A - B)= cos A cos B + sin Asin B then find
sin15 and cos 15 .

A = B = 60^{\circ}

cos (A - B) = cos A cos B + sin A sin B

sin (A - B) = sin A cos B - cos A sin B

tan (A - B) = \frac{tan A - tan B}{1 + tan A tan B}

Given that sin (A + B) = sin A cos B + cos A sin B, find the value of sin 75

Join BYJU'S Learning Program