Question

Cos 60 sin60 +cosec 60 + sec 60

Answer 1

Answer:

1/√2×√3/2+2/√3+2=3.76707297

Answer 2

Answer:

The value of $\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right)$ is $\frac{11 \sqrt{3}}{12}+2$.

Step-by-step explanation:

Given:

$\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right)$

To find:

The value of $\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right)$

Step 1

Let, $\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right)$

Here, by using trigonometric identities, we get the values of sin, cos, cosec, and tan

then

$&\csc \left(60^{\circ}\right)=\frac{1}{\sin \left(60^{\circ}\right)}$

$&=\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\frac{1}{\sin \left(60^{\circ}\right)}+\sec \left(60^{\circ}\right)$

Express with sin, cos

$&\sec \left(60^{\circ}\right)=\frac{1}{\cos \left(60^{\circ}\right)}$

$&=\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\frac{1}{\sin \left(60^{\circ}\right)}+\frac{1}{\cos \left(60^{\circ}\right)}$

Step 2

Use the following trivial identity:

$\cos \left(60^{\circ}\right)=\frac{1}{2}$

$\sin \left(60^{\circ}\right)=\frac{\sqrt{3}}{2}$

$\sin \left(60^{\circ}\right)=\frac{\sqrt{3}}{2}$

$\quad \cos \left(60^{\circ}\right)=\frac{1}{2}$

Step 3

Substituting the values of trivial identity, we get

$\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right)$

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

$\frac{1}{2} \cdot \frac{\sqrt{3}}{2}+\frac{1}{\frac{\sqrt{3}}{2}}+\frac{1}{\frac{1}{2}}=\frac{11 \sqrt{3}}{12}+2$

$=\frac{11 \sqrt{3}}{12}+2$

Therefore, the correct answer is

$\cos \left(60^{\circ}\right) \sin \left(60^{\circ}\right)+\csc \left(60^{\circ}\right)+\sec \left(60^{\circ}\right) =\frac{11 \sqrt{3}}{12}+2$.

#SPJ2