If cot α = 1 and sec β = - 5 3 , where π < α < 3 π 2 and π 2 < β < π , then the value of tan α + β and the quadrant in which α + β lies, respectively are

Given, cot α = 1 , sec β = - 5 3 So, cos β = - 3 5 , tan β = - 4 3 and tan α = 1 Now using formula tan α + β = tan α + tan β 1 - tan α tan β ⇒ tan α + β = 1 - 4 3 1 + 4 3 × 1 = - 1 7 We know that tan θ is negative in 2 n d & 4 t h quadrant but as π < α < 3 π 2 , so α + β will lie in IV th quadrant.

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minPYQ_2022

MathematicsMediumsingle choice

If $\cot α = 1$ and $\sec β = - \frac{5}{3}$ , where $π < α < \frac{3 π}{2}$ and $\frac{π}{2} < β < π$ , then the value of $\tan (α + β)$ and the quadrant in which $α + β$ lies, respectively are

Options:

Answer:

Solution:

Given,

$\cot α = 1, \sec β = \frac{- 5}{3}$

So, $\cos β = \frac{- 3}{5}, \tan β = \frac{- 4}{3}$ and $\tan α = 1$

Now using formula $\tan (α + β) = \frac{\tan α + \tan β}{1 - \tan α \tan β}$

$\Rightarrow \tan (α + β) = \frac{1 - \frac{4}{3}}{1 + \frac{4}{3} \times 1} = \frac{- 1}{7}$

We know that $\tan θ$ is negative in $2^{n d} & 4^{t h}$ quadrant but as $π < α < \frac{3 π}{2}$ , so $α + β$ will lie in ${IV}^{th}$ quadrant.

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2022

Doubts & Discussion

Loading discussions...

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2028 (Class 11)

JEE Main 2027 (Class 12+)