A student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?

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06-06-2022
Mathematics

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A student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?

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AshishdwivedilVTidn AshishdwivedilVTidn · Answer 1 · 2022-06-15T12:24:39-04:00

Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

What is Trigonometry?

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

Here,

tan²θ + 1 = sec²θ

sin²θ/cos²θ + 1 = 1/cos²θ

By taking LCM, we get

(sin²θ + cos²θ)/cos²θ = 1/cos²θ

(sin²θ + cos²θ) = cos²θ/cos²θ

(sin²θ + cos²θ) = 1

Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

Learn more about Trigonometry from:

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Sagot :

What is Trigonometry?

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