Question

prove this question in the image question related to trigonometry class 10​

Answer 1

Answer:

Trigonometry (mathematics): How do I prove [math]\csc \theta + \sin (-\theta) = \frac{\cos^2 \theta}{\sin \theta}[/math]?

Using trigonometric identity csc θ = 1/sin θ and formula sin (- θ) = sin (360⁰- θ), we have:

csc θ + sin (-θ) = (1/sin θ) + sin (360⁰- θ)

Now, using the formula: sin (α – β) = sin α cos β – cos α sin β, we have:

= (1/sin θ) + sin 360⁰cos θ – cos 360⁰sin θ

= (1/sin θ) + (0) cos θ – (1) sin θ

= (1/sin θ) + 0 – sin θ

= (1/sin θ) – (sin θ)(sin θ/sin θ)

= (1/sin θ) – (sin² θ)/sin θ

= (1 – sin² θ)/sin θ

Now, using the trigonometric identity cos² θ + sin² θ = 1, we have our desired result:

= cos² θ/sin θ

Answer 2

Answer:

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