Question

(sina-coseca)^2 +(cosa-seca)^2 = tan2a + cot2A - 1

Answer 1

Answer:

Step-by-step explanation:

(SinA - CosecA)² +(CosA - SecA)²

= Sin²A+ Cosec²A - 2SinACosecA + Cos²A + Sec²A - 2CosASecA

= (Sin²A + Cos²A) + Cosec²A + Sec²A - 4

= Cosec²A + Sec²A - 3

= (Cosec²A - 1) + (Sec²A - 1) - 1

= Cot²A + Tan²A - 1

=  R.H.S

Hence Proved.

Answer 2

Answer:

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Step-by-step explanation:$(sinA-cosecA)^{2}+(cosA-secA)^2=sin^2A+Cosec^2A+cos^2A+sec^2A-2sinAcosecA-2cosAsecA$

$=(sin^2A+cos^2A)+cosec^2A+sec^2A-2sinA\frac{1}{sinA}-2cosA\frac{1}{cosA}$

$=1+cosec^2A+sec^2A-2-2\\=cosec^2A+sec^2A-3$

=$(cosec^2A-1)+(sec^2A-1)-1$

$=(cot^2A)+(tan^2A)-1\\=tan^2A+cot^2A-1$

Hence,proved