Question

3 sin 3A + 2 cos 2A + 5 degree upon 2 cos 3A - sin 2A - 10 degree when a is equals to 20 evaluate​

Answer 1

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Answer 2

(3 sin 3A + 2 cos 2A + 5°) / (2 cos 3A - sin 2A - 10° )  = 3√3 + 2√2

Given:

(3 sin 3A + 2 cos 2A + 5°) / (2 cos 3A - sin 2A - 10° )  

And A = 20

To find:

Evaluate (3 sin 3A + 2 cos 2A + 5°) / (2 cos 3A - sin 2A - 10° )  

Solution:

Given (3 sin 3A + 2 cos 2A + 5°) / (2 cos 3A - sin 2A - 10° )  

And A = 20°

Given expression

= (3 sin 3(20) + 2 cos 2(20) + 5°) / (2 cos 3(20) - sin 2(20) - 10° )    

= (3 sin 60° + 2 cos 45°) / 2 cos 60° - sin 30°

From trigonometric table

sin 60° = √3/2   and  cos 60° = 1/2

sin 45° = 1/√2    and  cos 45° = 1/√2  

(3 sin 60° + 2 cos 45°) / 2 cos 60° - sin 30°  

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

= $\frac{\frac{3\sqrt{3} }{2}+ \frac{2}{\sqrt{2} } }{1 - \frac{1}{2} }$

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

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

= 3√3 + 2√2

Therefore,

(3 sin 3A + 2 cos 2A + 5°) / (2 cos 3A - sin 2A - 10° )  = 3√3 + 2√2

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