Question

Find the value of x.

Friends please solve ... nedd urgently.
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Answer 1

Answer:

Answer i = The value of x = 15

.

Answer ii = The value of x = 30

.

Answer iii = The value of x = 15

Answer 2

(i) tan 3x = sin 45° cos 45° + sin 30°

Solution:-

Take R.HS

$\sf \implies sin \: 45\degree \: cos \: 45\degree + sin\degree$

$\sf \implies \dfrac{1}{\sqrt{2}} \times \dfrac{1}{\sqrt{2}} + \dfrac{1}{2}$

$\sf \implies \dfrac{1}{2} + \dfrac{1}{2}$

$\sf \implies \bold{1}$

So,

$\sf \implies$ tan 3x = 1

We know ,

tan 45° = 1

Now,

$\sf \implies$ tan 3x = tan 45°

$\sf \implies$ 3x = 45°

$\sf \implies$ x = 45°/3

$\sf \implies$ x = 15°

Therefore,

Value of x is 15°

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(ii) cos x = cos 60° cos 30° + sin 60° sin 30°

Solution:-

Take R.H.S

$\sf \implies cos \: 60 \degree \: cos \: 30\degree + sin \: 60\degree \: sin \: 30\degree$

$\sf \implies \dfrac{1}{2} \times \dfrac{\sqrt{3}}{2} + \dfrac{\sqrt{3}}{2} \times \dfrac{1}{2}$

$\sf \implies \dfrac{\sqrt{3}}{4} + \dfrac{\sqrt{3}}{4}$

$\sf \implies \dfrac{\sqrt{3} + \sqrt{3}}{4}$

$\sf \implies \dfrac{2 \times \sqrt{3}}{4}$

$\sf \implies \bold{\dfrac{\sqrt{3}}{2}}$

So,

$\sf \implies$ cos x = √3/2

We know,

cos 30° = √3/2

Now,

$\sf \implies$ cos x = cos 30°

$\sf \implies$ x = 30°

Therefore,

Value of x is 30°.

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(iii) sin 2x = sin 60° cos 30° - cos 60° sin 30°

Solution:-

Take R.H.S

$\sf \implies sin \: 60\degree \:cos \: 30\degree - cos \: 60\degree \: sin\:30\degree$

$\sf \implies \dfrac{\sqrt{3}}{2} \times \dfrac{\sqrt{3}}{2} - \dfrac{1}{2} \times \dfrac{1}{2}$

$\sf \implies \dfrac{3}{4} - {1}{4}$

$\sf \implies \dfrac{3 - 1}{4}$

$\sf \implies \dfrac{2}{4}$

$\sf \implies \bold{ \dfrac{1}{2} }$

So,

$\sf \implies$ sin 2x = 1/2

We know,

sin 30° = 1/2

Now,

$\sf \implies$ sin 2x = sin 30°

$\sf \implies$ 2x = 30°

$\sf \implies$ x = 30°/3

$\sf \implies$ x = 15°

Therefore,

Value of x is 15°.