Question

if A is equal to 60degree B is equal to 30 degree find the value of {sin A cos B +cos A sin B}² - (cos A cos B - sin A sin B)²​

Answer 1

Answer: 1

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Answer 2

Answer:

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}} \\ \small\bold\red{{(sin A cos B +cos A sin B)}² - (cos A cos B - sin A sin B)²} \\ \small\bold\blue{Put A = 60° and B = 30°} \\ \small\bold\red{{ = (sin 60 cos 30 +cos 60 sin 30)}² - (cos 60 cos 30 - sin 60 sin 30)²} \\ \small\bold\red{ = {( \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} ) }^{2} - {( \frac{1}{2} \times \frac{ \sqrt{3} }{2} - \frac{1}{2} \times \frac{3}{2} )}^{2} } \\ \small\bold\red{ = {( \frac{3}{4} + \frac{1}{4} )}^{2} - 0} \\ \small\bold\red{ = 1}$