Question

sin (90° + A) sin (180° - A) tan (180° - A)
Cos (360° - A) cos (180° - A) tan (180° + A)​

Answer 1

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Trigonometrical Ratios of (180° + θ)

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What are the relations among all the trigonometrical ratios of (180° + θ)?

In trigonometrical ratios of angles (180° + θ) we will find the relation between all six trigonometrical ratios.

We know that,

sin (90° + θ) = cos θ

cos (90° + θ) = - sin θ

tan (90° + θ) = - cot θ

csc (90° + θ) = sec θ

sec ( 90° + θ) = - csc θ

cot ( 90° + θ) = - tan θ

Using the above proved results we will prove all six trigonometrical ratios of (180° + θ).

sin (180° + θ) = sin (90° + 90° + θ)

= sin [90° + (90° + θ)]

= cos (90° + θ), [since sin (90° + θ) = cos θ]

Therefore, sin (180° + θ) = - sin θ, [since cos (90° + θ) = - sin θ]