Question

prove that root 1-cos a /1+cos a=1/cosec a + cot a

Answer 1

Answer:

√1+cosA/√1-cosA

Multiplying and dividing with conjugate of denominator

{√1+cosA/√1-cosA} × {√1+cosA/√1+cosA}

(√1+cosA)(√1+cosA) / (√1-cosA)(√1+cosA)

{√(1+cosA)(1+cosA)} / {√(1-cosA)(1+cosA)}

{√(1+cosA)²} / {√(1-cosA)(1+cosA)}

Since(a-b)(a+b) = a² - b²

Therefore (1-cosA)(1+cosA) = 1² - cos²A

(1+cosA) / √(1² - cos²A)

Now 1 - cos²A = sin²a

Thus (1+cosA) / √(sin²a)

(1+cosA) / sinA

Splitting the numerator

1/sinA + cosA/sinA

1/sinA = cosecA and cosA/sinA = cotA

Thus

1/sinA + cosA/sinA = cosecA + cotA