What is the value of \sin(2\theta) ? I. \tan\theta+\cot\theta=3 II. (\cosec\theta+\cot\theta)(\cosec\theta-\cot\theta)=1

Correct Answer is : if the statement I alone is sufficient to answer the question.

if the statement I alone is sufficient to answer the question.

if the statement II alone is sufficient to answer the question.

if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

if both the statements I and II together are not sufficient to answer the question and additional data is required.

AP ICET 2015 Paper

Question : 3 of 200

Marks: +1, -0

What is the value of

\sin(2θ)

?
I.

\tanθ+\cotθ=3

II.

(\cosecθ+\cotθ)(\cosecθ-\cotθ)=1

if the statement I alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

I. Given:

\tanθ+\cotθ=3

⇒{\sinθ}/{\cosθ}+{\cosθ}/{\sinθ}=3

⇒{\sin^{2}θ+\cos^{2}θ}/{\sinθ\cosθ}=3

⇒{1}/{\sinθ\cosθ}=3

⇒2\sinθ\cosθ={2}/{3}

⇒\sin2θ={2}/{3}

∴ I alone is sufficient.

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