Answer:
option b)
tan²θ + 1 = sec²θ
Step-by-step explanation:
The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.
hypotenuse² = height² + base²
Given in the questions are some pythagorus identities which except of b) are all incorrect as explained below.
1)
sin²θ + 1 = cos²θ incorrect
sin²θ + cos²θ = 1 correct
2)
by dividing first identity by cos²θ
sin²θ/cos²θ + cos²θ/cos²θ = 1/cos²θ
tan²θ + 1 = sec²θ correct
3)
1 - cot²θ = cosec²θ incorrect
by dividing first identity by sin²θ
sin²θ/sin²θ + cos²θ/sin²θ = 1/sin²θ
1 + cot²θ = cosec²θ correct
4)
1 - cos²θ = tan²θ
not such pythagorus identity exists
