Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + cot² x = csc²x and csc x = [tex]\frac{1}{sinx}[/tex]
• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Consider the left side
sin²Θ( 1 + cot²Θ )
= sin²Θ × csc²Θ
= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified
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cos²Θ - sin²Θ
= cos²Θ - (1 - cos²Θ)
= cos²Θ - 1 + cos²Θ
= 2cos²Θ - 1 = right side ⇒ verified
