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Simplify sin theta csc theta - sin^2 thetacos^2 thetasin^2 theta2 sin^2 theta1pls help
4 months ago
Q:
simplify sin theta csc theta - sin^2 thetacos^2 thetasin^2 theta2 sin^2 theta1pls help
Accepted Solution
A:
Answer:The answer is cos²Ф ⇒ first answerStep-by-step explanation:* Lets talk about the trigonometry functions- sin²Ф + cos²Ф=1 ⇒ subtract cos²Ф from each side∴ sin²Ф = 1 - cos²Ф- sin²Ф + cos²Ф=1 ⇒ subtract sin²Ф from each side∴ cos²Ф = 1 - sin²Ф- cscФ = 1/sinФ ⇒ cscФ × sinФ = (1/sinФ) × sinФ = 1* Now lets solve the problem sinФ × cscФ - sin²Ф∵ sinФ × 1/sinФ = 1∴ sinФ × cscФ - sin²Ф = 1 - sin²Ф∵ 1 - sin²Ф = cos²Ф∴ sinФ × cscФ - sin²Ф = cos²Ф* The answer is cos²Ф