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Answer:
2.612
Step-by-step explanation:
To evaluate the expression cos 45° / sec 30° + cosec 30°, we can follow these steps:
First, let's calculate cos 45°. The cosine of 45 degrees is equal to √2/2, which is approximately 0.707.
Next, let's calculate sec 30°. The secant of an angle is the reciprocal of the cosine of that angle. So, sec 30° is equal to 1/cos 30°. The cosine of 30 degrees is √3/2, so sec 30° is 1/(√3/2), which simplifies to 2/√3 or (√3/3)_2. Multiplying (√3/3) by 2, we get (√3/3)_2 = 2√3/3, which is approximately 1.155.
Now, let's calculate cosec 30°. The cosecant of an angle is the reciprocal of the sine of that angle. The sine of 30 degrees is 1/2, so cosec 30° is equal to 1/(1/2), which simplifies to 2.
Now, we can substitute these values back into the original expression:
cos 45° / sec 30° + cosec 30°
0.707 / 1.155 + 2
Calculating the division first, we get:
0.612 + 2
Adding these two values together, we get:
2.612
So, cos 45° / sec 30° + cosec 30° is approximately equal to 2.612.
Verified answer
Answer:
Step-by-step explanation:
since cos 45= 1 , sec30= 2/[tex]\sqrt{3}[/tex] and cosec 30 =2
now put the values
1
------------------
2 2
------ + --------
[tex]\sqrt{3}[/tex] 1
= 1
------------------
2 + 2 [tex]\sqrt{3}\\[/tex]
--------------------
[tex]\sqrt{3}[/tex]
= [tex]\sqrt{3}\\\\[/tex]
-------------
2 + 2[tex]\sqrt{3}\\[/tex]
now rationaise it
[tex]\sqrt{3}\\[/tex] [ 2 - 2[tex]\sqrt{3}[/tex] ]
------------------------
[tex](2 + 2\sqrt{3} ) ( 2 - 2\sqrt{3} )[/tex]
2[tex]\sqrt{3}[/tex] - 6
= ------------
2² - [2[tex]\sqrt{3}[/tex]]²
2[tex]\sqrt{3}[/tex] - 6
= ----------------------
4 - 12
= 2 [tex]\sqrt{3}[/tex] - 6
---------------
- 6
= 6 - 2[tex]\sqrt{3}[/tex]
--------------
4
= 3 - [tex]\sqrt{3}[/tex]
------------------
2