Question

Determine the value of x : 2 cosec2 300 + x sin 2 60 0 –¾ tan 2 30 0 = 10

Answer 1

2cosec

2

30

∘

+xsin

2

60

∘

−

4

3

tan

2

30

∘

=10

L.H.S:2(2)

2

+x(

2

3

)

2

−

4

3

(

3

1

)

2

=10 [∵cosec30

∘

=2,sin60

∘

=

2

3

,tan30

∘

=

3

1

]

⇒8+

4

3x

−

4×3

3

=10

⇒8+

4

3x

−

4

1

=10

⇒

4

32+3x−1

=10

⇒3x+31=40

⇒3x=40−31

⇒3x=9

⇒x=

3

9

⇒x=3