Question

please answer with method ​

Answer 1

Answer:

Step-by-step explanation: the value of cos for 1/2 is 60°

The value for tan 1/√3 is 30°

So( alpha +beta ) is equal to 90°

And sin90° = 1

Answer 2

Answer : Option (D) is correct✔️

Solution :

Given that :

$\cos \alpha = \frac{1}{2} \: and \\ \\ \tan\beta = \frac{1}{ \sqrt{3} } = \frac{p}{b} \\ \\ = > {h}^{2} = {p}^{2} + {b}^{2} \\ \\ = > {h}^{2} = 1 + 3 = 4 \\ \\ = h = 2 \\ \\ \sin\beta = \frac{p}{h} = \frac{1}{2} \: and \: \cos\beta = \frac{b}{h} = \frac{ \sqrt{3} }{2}$

And

$\cos\alpha = \frac{1}{2} = \frac{b}{h} \\ \\ = > {h}^{2} = {p}^{2} + {b}^{2} \\ \\ = > {2}^{2} = {p}^{2} + 1 \\ \\ = > {p}^{2} = 4 - 1 = 3 \\ \\ = > p = \sqrt{3} \\ \\ = > \sin \alpha = \frac{p}{h} = \frac{ \sqrt{3} }{2}$

Now,

$\sin( \alpha + \beta ) = \sin\alpha \cos\beta + \cos \alpha \sin\beta \\ \\ = > \sin( \alpha + \beta ) = \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} \\ \\ = > \sin( \alpha + \beta ) = \frac{3}{4} + \frac{1}{4} \\ \\ = > sin( \alpha + \beta ) = 1$

I hope it will be helpful for you ✌️✌️

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Fóllòw MË ☺️☺️