Question

tan^2a-7sin^3a=k.
sin^3a+tan^2a=k+1.
find the value of a​

Answer 1

Answer:

tan^2a-7sin^3a=k.

sin^3a+tan^2a=k+1.

Step-by-step explanation:

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Question

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If

tanA

tan3A

=k, then

sinA

sin3A

is equal to

Hard

Solution

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Correct option is

C

k−1

2k

,k



∈(

3

1

,3)

Using tan3A=

1−3tan

2

A

3tanA−tan

3

A

We get

tanA

tan3A

=k=

1−3tan

2

A

3−tan

2

A

So, tan

2

A=

1−3k

k−3

=

1−sin

2

A

sin

2

A

So, sin

2

A=

4(k−1)

k−3

Now,

sinA

sin3A

=

sinA

3sinA−4sin

3

A

=3−4sin

3

A=3−

1−k

k−3

=

k−1

2k

Now, tan

2

A>0

So,

3k−1

k−3

>0

So, k<

3

1

or k>3