Let θ ∈ ( 0 , 4 π ) and t 1 = ( tan θ ) t a n θ , t 2 = ( tan θ ) c o t θ and t 4 = ( cot θ ) t a n θ , then

As when θ ∈ ( 0 , 4 π ) tan θ 1 ∴ ( tan θ ) c o t θ 1 ∴ t 4 > t 1 which only holds in option (b).

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesBasic Identities & T RatiosEasy2 minPYQ_2006

MathematicsEasysingle choice

Let $θ \in (0, \frac{π}{4})$ and $t_{1} = (tan θ)^{t a n θ}, t_{2} = (tan θ)^{c o t θ}$ and $t_{4} = (cot θ)^{t a n θ}$ , then

Options:

Answer:

Solution:

As when $θ \in (0, \frac{π}{4})$ $tan θ < cot θ$ Since, $tan θ < 1$ and $cot θ > 1$ $∴ (tan θ)^{c o t θ} < 1$ and $(cot θ)^{t a n θ} > 1$ $∴ t_{4} > t_{1}$ which only holds in option (b).

Stream:JEE_ADVSubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Basic Identities & T Ratios

⏱ 2mℹ️ Source: PYQ_2006

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