Question

Prove that cosec A (1-cosA) (cosecA + cot) = 1​

Answer 1

Answer:

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Answer 2

Answer:

To prove- √(1+cosA)/√(1-cosA)=cosecA + cot A

Proof-

LHS-

√(1+cosA)/√(1-cosA)

Multiplying with √(1+cosA) on both numerator and denominator, we have,

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

=[√{(1+cosA)*(1+cosA)}]/[√{(1-cosA)*(1+cosA)}]

={√(1+cosA)²}/{√(1²-cos²A)}

=(1+cosA)/√(sin²A)

=(1+cosA)/sinA

=(1/sinA)+(cosA/sinA)

=cosecA + cotA

Hence proved