If sin A+ cos A=4/3 , then find the value of tan A + cot A.

SSC Selection Post 2024 PYQ — Question 52

If $sin A+ cos A=\frac{4}{3}$ , then find the value of tan A + cot A.

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{18}{7}$ .

Given, sinA + cosA = 4/3

⇒ (sinA + cosA)² = 16/9

⇒ 1 + 2sinAcosA = 16/9

⇒ sinAcosA = 7/18

Now, tanA + cotA = 1/sinAcosA

⇒ tanA + cotA = 18/7