Question

(cosec A + sin A)(cosec A - sin A ) = cot^2A + cos^2A
Prove .

Answer 1

Answer:

Prove that:

(cosec A+sin A)(cosec A-sin A)=cot²A+cos²A

L.H.S=(cosec A+sin A)(cosec A-sin A)

=cosec²A -sin²A .....[(a+b)(a-b)=a²-b²]

=1+cot²A-(1-cos²A) .....(cosec²A=1+cot²A and

sin²A=1-cos²A)

=1+cot²A-1+cos²A

=cot²A+cos²A

therefore:

(cosec A + sin A)(cosec A-sin A)=cot²A+cos²A