Question

The value of the expression (√3sin75∘−cos75∘) is

Answer 1

Answer:

√2 is the answer

Step-by-step explanation:

please mark me as brainliest

Answer 2

Answer:

The value of ($\sqrt{3}$sin75° - cos 75°) is $\sqrt{2}$ .

Step-by-step explanation:

Explanation:

Given , ($\sqrt{3}$sin75° - cos 75°)

So, this can be written as ,

[$\sqrt{3}$sin(45° + 30° ) - cos (45° - 30°)]

And we know that the formula of sin(A + B) and cos(A +B),

sin(A + B) = sinA cosB + cos A sinB  

and cos (A + B) = cosAcosB - sinAsinB.

Step 1:

From the question we have,

[$\sqrt{3}$sin(45° + 30° ) - cos (45° - 30°)]

Now, from the formula of sin(A + B) and cos (A + B ) we get,

[$\sqrt{3}${sin(45°)cos 30° + cos 45° sin30  } - {cos 45° cos 30° - sin45° sin30°] .....(i)

Step 2:

And the value of sin45 = $\frac{1} {\sqrt{2} }$ , cos 45 = $\frac{1}{\sqrt{2} }$ , sin30 = $\frac{1}{2}$ and cos30 = $\frac{\sqrt{3} }{2}$ .

On putting all these value in (i) we get,

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

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

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

⇒$\frac{3 + \sqrt{3} - (\sqrt{3} - 1 ) }{2\sqrt{2} }$ = $\frac{4}{2\sqrt{2} }$ = $\sqrt{2}$ .

Final answer:

Hence, the value of ($\sqrt{3}$sin75° - cos 75°) is $\sqrt{2}$ .

#SPJ3