Question

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Answer 1

Answer:

The right choice is option (B) tan²θ + 1 = sec²θ

Step-by-step explanation:

1 + (sin²θ/cos²θ)  

= (cos²θ/cos²θ) + (sin²θ/cos²θ)

= (cos²θ + sin²θ) / cos²θ

= 1/cos²θ

= sec²θ

Answer 2

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