Question

7. Without using trigonometric table, evaluate:
cos 60° + sin 30° - cot 30° divided by
tan 60° + sec 45° - cosec 45°​

Answer 1

Answer:

Step-by-step explanation:

sin(90-60)-cot30/cot(90-60)+cosec(90-45)-cosec45

sin30+sin30-cot30/cot30+cosec45-cosec45

2sin30-cot30/cot30

Answer 2

The value of $\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$ is equal to $\dfrac{2\sin 30-\cot 30}{\tan 60}.$

Step-by-step explanation:

We have,

$\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$

To find, the value of $\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$ = ?

∴ $\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$

$=\dfrac{\cos (90 -30)+\sin 30-\cot 30}{\tan 60+\sec (90-45)-\csc 45​}$

Using the trigonometric identity,

$\sin A=\cos (90 -A)$ and $\csc A = \sec (90-A)$

$=\dfrac{\sin 30+\sin 30-\cot 30}{\tan 60+\csc 45-\csc 45​}$

$=\dfrac{2\sin 30-\cot 30}{\tan 60}$

∴ The value of $\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$ $=\dfrac{2\sin 30-\cot 30}{\tan 60}$

Thus, the value of $\dfrac{\cos 60+\sin 30-\cot 30}{\tan 60+\sec 45-\csc 45​}$ is equal to $\dfrac{2\sin 30-\cot 30}{\tan 60}.$