Question

prove √( 1-cos A/1+cos A) = cosec A - cot A

Answer 1

Answer:

we have to prove that

√(1-cos A/1+cos A) = cosec A - cot A

LHS:

√( 1-cos A/1+cos A)

• √(1-cos A/1+cosA×1-cos A/1-cos A)
• √[(1-cos A )^2]/1^2-cos A^2 (a+b)(a-b)=a^2-b^2 (a-b)^2=a^2+b^2-2ab
• √[(1-cos A )^2]/sin^2
• then square _roots become cancel
• 1-cos A/sin A
• 1/sin A-cos A/ sin A
• cosec A- cot A =RHS 1/sin A=cosec A

cos A/sin A= cot A

then

√ 1-cos A/1+cos A) = cosec A - cot A