Question

if 2x tan^260°+3x sin^230°=27cos^2 45°/4sin^260°.find the value of x.​

Answer 1

Step-by-step explanation:

2 x tan²60° + 3 x sin²30° = ( 27 cos²45° ) / 4 sin²60° )

In the attachment , I have given the trigonometric table .

From there we have :

tan 60° = √3

sin 30° = 1/2

cos 45° = 1 /√2

sin 60° = √3 / 2

Hence we can write the above equation as :

2 x ( √3 )² + 3 x ( 1/2 )² = ( 27 × ( 1/√2 )² ) / ( 4 × ( √3/2 )² )

⇒ 2 x × 3 + 3 x × 1/4 = ( 27/2 / 3 )

⇒ 6 x + 3 x /4 = 9/2

⇒ 2 x + x/4 = 3/2

⇒ x ( 2 + 1/4 ) = 3/2

⇒ x ( 8 + 1 )/4 = 3/2

⇒ x × 9/4 = 3/2

⇒ x = 3/2 × 4/9

⇒ x = 2/3

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