Question

If tanθ+ cotθ= 2, find the value of tan2 θ + cot2 θ

Answer 1

Answer:

tanθ+cotθ=2

Squaring both sides;

(tanθ+cotθ)

2

=2

2

⇒tan

2

θ+cot

2

θ+2tanθcotθ=4

⇒tan

2

θ+cot

2

θ+2=4

⇒tan

2

θ+cot

2

θ=2

Answer 2

tanA + cotA = 2

tanA = 2-cotA

=> tan²A + cot²A

substituting above value of tanA

(2-cotA)² + cot²A

4 - 2cot²A + cot²A +cot²A

4 - 2cot²A +2cot²A

4