Question

prove the question 1 -cos A/1+cosA = (cot A - cosec A) ppower2​

Answer 1

Step-by-step explanation:

1-cosA/1+cosA

=1-cosA/1+cosA×1-cosA/1-cosA

=(1-cosA)²/1-cos²A

=1-2cosA+cos²A/sin²A

=1/sin²A-2cosA/sin²A+cos²A/sin²A

=cosec²A-2×1/sin²A.cosA/sinA+cot²A

=cosec²A-2cosecAcotA+cot²A

=(cosecA-cotA)²

={-(cotA-cosecA)}²

=(cotA-cosec)²

=RHS. (proved)

or

(cotA-cosecA)²

={-(cscA-cotA)}²

=(cscA-cotA)²

=(1/sinA-cosA/sinA)²

=(1-cosA/sinA)²

=(1-cosA)²/sin²A

=(1-cosA)(1-cosA)/1-cos²A

=(1-cosA)(1-cosA)/(1+cosA)(1-cosA)

=1-cosA/1+cosa

=LHS. (proved)