Question

if root 2 sin theta is equal to 1 find sec square theta minus cosec square theta and not by using values by Pythagoras Theorem​

Answer 1

Solution :-

√2sinθ = 1

⇒ sinθ = 1/√2 = Opposite side / Hypotenuse

Comparing on both sides

• Opposite side = 1
• Hypotenuse = √2

Let the adjacent side be x

By Pythagoras theorem

(Adjacent side)² + (Opposite side)² = (Hypotenuse)²

⇒ x² + 1² = (√2)²

⇒ x² + 1 = 2

⇒ x² = 2 - 1

⇒ x² = 1

⇒ x = 1

⇒ Adjacent side = 1

• secθ = Hypotenuse / Adjacent side = √2 / 1
• cosecθ = Hypotenuse / Opposite side = √2 / 1

Now, sec²θ - cosec²θ

= (√2)² - (√2)²

= 2 - 2

= 0

Therefore the value of sec²θ - cosec²θ is 0.

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Answer 2

Step-by-step explanation:

see the attachment...