Question

sin3ϴ/sinϴ-cos3ϴ/cosϴ=2

Answer 1

Answer:

Given: [sin(3θ)/sinθ-cos(3θ)/cos(θ)] = 2

=   [sin(3θ)cos(θ)−cos(3θ)sin(θ)]/[sin(θ)cos(θ)]

=   [sin(3θ−θ)]/[sin(θ)cos(θ)]

=   [sin(2θ]/[sin(θ)cos(θ)]

=   [2 sin(θ)cos(θ)]/[sin(θ)cos(θ)]

=   2

Answer 2

3 is the right answer

Step-by-step explanation:

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Using trigonometric identity:

sin3θ=3sinθ−4sin

3

θ⇒sin

3

θ+sin3θ=3sinθ−3sin

3

θ

cos3θ=4cos

3

θ−3cosθ⇒cos

3

θ−cos3θ=3cosθ−3cos

3

θ

Taking L.H.S.-

cosθ

cos

3

θ−cos3θ

+

sinθ

sin

3

θ+sin3θ

=

cosθ

3cosθ−3cos

3

θ

+

sinθ

3sinθ−3sin

3

θ

=

cosθ

3cosθ(1−cos

2

θ)

+

sinθ

3sinθ(1−sin

2

θ)

=3sin

2

θ+3cos

2

θ

=3(sin

2

θ+cos

2

θ)

=3 =R.H.S

Hence Proved