Question

find the value of x in √3 tan 2x = cos 60 +sin 45 cos 45​

Answer 1

Step-by-step explanation:

Given

3

tan2x=cos60

∘

+sin45

∘

cos45

∘

3

tan2x=

2

1

+(

2

1

×

2

1

) [∵cos60

∘

=

2

1

,cos45

∘

=sin45

∘

=

2

1

]

3

tan2x=

2

1

+

2

1

3

tan2x=1

tan2x=

3

1

we know that

tan30

∘

=

3

1

tan2x=tan30

∘

2x=30

∘

∴x=15

∘

Answer 2

Given :

√3 tan 2x = cos60 + sin45 cos45

Answer :

$\sf{ √3tan \: 2x = 1/2+(1/√2×1/√2) }$

$\sf{ therefore, cos60 = 1/2, cos45 = sin45 = 1/2) }$

$\sf{ √3tan \: 2x=1/2+1/2 }$

$\sf{ √3tan \: 2x = 1 }$

$\sf{ tan2x=1/√3 }$

$\sf\large\underline\bold \red{ we \: know \: that }$

$\sf{ tan30 \: =1/√3 }$

$\sf{ tan2x \: = tan30 }$

$\sf{ 2x \: = 30 }$

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