Question

Cosec + Cot = y then prove that: cos = y^2-1/y^2+1

Answer 1

Step-by-step explanation:

Given Cosec + Cot = y then prove that: cos = y^2-1/y^2+1

• Given cosec + cot = y
• We know that
• Cosec^2 – cot^2 = 1
• This is in the form of a^2 – b^2 = (a + b)(a – b)
• (Cosec + cot)(cosec – cot) = 1
• So cosec – cot = 1/y
• Cosec + cot = y
• Now 2 cosec = y + 1/y
• 2cosec = y^2 + 1 / y
• Now cosec = y^2 + 1 / 2y
• Or 1 / sin = y^2 + 1 / 2y
• Or sin = 2y / y^2 + 1
• Squaring we get
• Sin^2 = 4y^2 / (y^2 + 1)^2
• 1 – sin^2 = cos^2
• Or cos = (y^2 – 1)^2 (y^2 + 1)

Reference link will be

https://brainly.in/question/1285074