Question

If cot x = sin 30 degrees + sin 45 degrees then find the value of x ?​

Answer 1

Answer:

R.H.S

sin45⋅cos45

o

+sin30

=

2

1

.

2

1

+

2

1

=

2

1

+

2

1

=

2

2

=1

Now,

L.H.S

tan3x=1

But tan45

o

=1

∴tan3x=tan45

⇒3x=45

⇒x=

3

45

∴x=15.

Answer 2

Given: $cot(x) \ = \ sin(30^{o}) + sin(45^{o})$

To find: the value of $x$

Solution:

We have, $cot(x) \ = \ sin(30^{o}) + sin(45^{o})$

We know that $sin(30^{o}) \ = \ \frac{1}{2}$ and $sin(45^{o}) \ = \ \frac{1}{\sqrt{2}}$; substituting these two values in the above expression, we will have:

$cot(x) \ = \ \frac{1}{2} \ + \ \frac{1}{\sqrt{2}}$

$\Rightarrow cot(x) \ = \ \frac{1}{2} \ + \ \frac{\sqrt{2}}{2}$

$\Rightarrow cot(x) \ = \ \frac{1 + \sqrt{2} }{2}$

Multiplying $cot^{-1}$ on both sides in the above expression, we get:

$\Rightarrow x \ = \ cot^{-1} (\frac{1 + \sqrt{2} }{2})$

$\Rightarrow x \ = \ cot^{-1} (1.207)$

$\Rightarrow x \ = \ 39.642^{o}$

Hence, the value of x is $39.642^{o}$