Question

Solve :cosec thita =cot thita + root 3



​

Answer 1

Answer:

cotθ+cosec θ=

3

sin θ

cosθ

+

sin θ

1

=

3

Taking square both side,

cos

2

θ+1+2cosθ=3−3cos

2

θ [\sin ce sin

2

θ=1−cos

2

θ]

4cos

2

θ+2cosθ−2=0

4cos

2

θ+4cosθ−2cosθ−2=0

We get

(cosθ+1)(4cosθ−2)=0

When,

(cosθ+1)=0

cosθ=−1

cosπ=cos(2n+1)π=−1

Hence θ=(2n+1)π.

When,

(4cosθ−2)=0

cosθ=

2

1

cos

3

π

=cos(2nπ±

3

π

)=

2

1

Hence, θ=(2nπ±

3

π

)

Step-by-step explanation:

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Answer 2

$\csc(x) = \cot(x) + \sqrt{3} \\ = \\ \frac{1}{ \sin(x) } = \frac{ \cos(x) }{ \sin(x) } \\ = \\ \sin(x) = \cos(x) \sin(x) \\ = \\ \cos(x) = 1$

therefore x= 0°