Question

cos60sin30+sin60cos30?? ​

Answer 1

Answer:

sin(30+60)=sin30cos60+cos30sin60

so the ans is 1

Answer 2

★To find:-

• Value of cos60°sin30°+sin60°cos30°

★Solution:-

From the trigonometry table,

✦Cos 60°= 1/2

✦Sin 60° = √3/2

✦Cos 30° = √3/2

✦Sin 30° = 1/2

Putting values,

$\displaystyle \sf \implies cos\ 60^\circ .sin\ 30^\circ + sin\ 60^\circ .cos\ 30^\circ$

$\displaystyle \sf \implies \bigg( \frac{1}{2} \times \frac{1}{2} \bigg)+\bigg( \frac{\sqrt{3} }{2} \times \frac{\sqrt{3} }{2} \bigg)$

$\displaystyle \sf \implies \frac{1}{4} +\frac{3}{4}$

$\displaystyle \sf \implies \frac{4}{4}$

$\displaystyle \implies \underline{\boxed{\sf 1.}}$

Alternative method:-

Using the formula,

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

Also,

✦Sin 90° = 1

Where,

• A = 60°
• B = 30°

Putting values,

➺(sin 60°)(cos 30°)+ (cos 60°)(sin 30°)

➺sin (60° +30°)

➺sin 90°

➺1 .

Hence,the required answer is 1.

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