Math, asked by hotelllrenukanahan, 10 months ago

evaluate sin 60° cos 30° + cos 30 sin 60°​

Answers

Answered by MoodyCloud
12

To evaluate:-

  • sin 60° cos 30° + cos 30° sin 60°

Solution:-

 \bigstar  \sf  \:sin  \: 60 \degree\: cos \: 30 \degree + cos \: 30  \degree  \: sin \: 60 \degree

Sin 60° = 3/2

Cos 30° = 3/2

Put the values,

 \implies \sf  \dfrac{ \sqrt{3} }{2}  \times  \dfrac{ \sqrt{3} }{2}  +  \dfrac{ \sqrt{3} }{2}  \times  \dfrac{ \sqrt{3} }{2}

 \implies \sf  \dfrac{3}{4}   +  \dfrac{3}{4}

 \implies \sf \dfrac{3 + 3}{4}

 \implies \sf  \dfrac{ \cancel{6}}{ \cancel{4}}

 \implies \sf  \dfrac{3}{2}

Therefore,

 \large \bigstar  \sf  \:sin  \: 60 \degree\: cos \: 30 \degree + cos \: 30  \degree  \: sin \: 60 \degree =  \dfrac{3}{2}

Answered by rathoreanushka92
2

Answer:

1

Step-by-step explanation:

Since, sin A = cos ( 90 - A ),

sin 60° . cos 30° + cos 60° . sin 30

= sin 60° . sin ( 90° - 30° ) + cos 60° . cos ( 90° - 30° )

= sin 60° . sin 60° + cos 60° . cos 60°

= sin^2 60° . cos^2 60°

= 1

( as sin^2 A + cos^2 A = 1 )

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