JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q20

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MathematicsSingle correct+4 / -1Question 20 of 90

If $\cot\alpha=1$ and $\sec\beta=-\dfrac53$ , where $\pi<\alpha<\dfrac{3\pi}2$ and $\dfrac\pi2<\beta<\pi$ , then the value of $\tan(\alpha+\beta)$ and the quadrant in which $\alpha+\beta$ lies, respectively are :

-\dfrac17

and IV

^{\text{th}}

quadrant

7 and I

^{\text{st}}

quadrant

-7

and IV

^{\text{th}}

quadrant

\dfrac17

and I

^{\text{st}}

quadrant

Answer and worked solution

Official answer: A

Values. $\tan\alpha=1$ ( $\alpha=225°$ ); $\cos\beta=-\frac35$ , $\tan\beta=-\frac43$ ( $\beta\approx126.9°$ ).

Sum. $\tan(\alpha+\beta)=\dfrac{1-\frac43}{1+\frac43}=-\frac17$ , and $\alpha+\beta\approx351.9°$ : fourth quadrant.

(A)

Topics:Trigonometric ratios and identities

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JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 20