Question

2tan3theta cos3theta - tan3theta - 2cos3theta + 1 = 0​

Answer 1

Answer:

2cos3θ=1

⇒cos3θ=

2

1

⇒cos3θ=cos60

Therefore, 3θ=60

⇒θ=20

(ii) 2

3

tanθ=6

⇒tanθ=

2

3

6

⇒tanθ=

3

×

3

3×

3

⇒tanθ=

3

(iii)

1+tan

2

θ

1−tan

2

θ

=

2

1

⇒

sec

2

θ

1−tan

2

θ

=

2

1

⇒

sec

2

θ

1−

cos

2

θ

sin

2

θ

=

2

1

⇒

cos

2

θ×sec

2

θ

cos

2

θ−sin

2

θ

=

2

1

⇒

sec

2

θ

1

×sec

2

θ

cos

2

θ−sin

2

θ

=

2

1

⇒cos

2

θ−sin

2

θ=

2

1

⇒cos

2

θ−1+cos

2

θ=

2

1

⇒2cos

2

θ=

2

1

+1

⇒2cos

2

θ=

2

3

⇒cos

2

θ=

4

3

⇒cosθ=

4

3

⇒cosθ=

2

3

.....[Since

2

3

]

⇒cosθ=30