Question

3 B
Show that : sec? o x cosec2 0 = sec 0 + cosec? O​

Answer 1

Answer:

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Answer 2

            Method 1

⇒ sec²θ.cosec²θ

⇒ (1/cos²θ) × (1/sin²θ)

⇒ 1/(cos²θ.sin²θ)

⇒ (sin²θ + cos²θ)/sin²θ.cos²θ

⇒ (sin²θ)/sin²θcos²θ + cos²θ/sin²θcos²θ

⇒ 1/cos²θ + 1/sin²θ

⇒ sec²θ + cosec²θ

Proved

        Method 2

sec²θ.cosec²θ = (tan²θ + 1)(cot²θ + 1)

       = tan²θcot²θ + tan²θ + cot²θ + 1

       = 1 + tan²θ + cot²θ + 1

       = (1 + tan²θ) + (1 + cot²θ)

       = sec²θ + cosec²θ

Proved