Question

WHAT IS (tanA+cotA) IF A=2pie/3.

Answer 1

Answer:

Step-by-step explanation:

SEE HERE .....

A=2π÷3

SO A=120'

NOW

=(tanA+cotA)

=tan(120)+cot(120)

WE HAVE TO FIND THE VALUE FOR TAN120 AND COT 120.....

tan(90×1+30)= -cot30. because cot 30 lies in 2nd quadrant....

similarly.....

cot(90×1+30)=-tan30 reason is same as above.........

putting values for -tan30= -1/√3

-cot 30= -√3

solving we get -4/√3

thanks and pls mark as branliest.....

Answer 2

ANSWER:

Given

• tanA + cotA = ?
• A = 2π/3

tanA + cotA

Simplifying we get

➜ sinA /cosA + cosA/sinA

➜ sin²A + cos²A/cosAsinA

We know that

sin²A + cos²A = 1

➜ 1/cosA.sinA

➜ 1/cosA × 1/sinA

➜ secA.cosecA

Given A = 2π/3

Convert → Degrees

π = 180°

2×180/3 = 120° = 90° + 30°

Substitute we get

➸ sec(120°).cosec(120°)

➸ sec(90° + 30°).cosec(90° + 30°)

Using

→ sec(90° + θ) = - cosecθ

→ cosec(90° + θ) = secθ

➸ - cosec30°. sec30°

➸ - 2 × 2/√3

➸ -4/√3