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(sin A +cosec A) square + (cos A +sec A) square =7+tan A square + cot A square

(sin A +cosec A) square + (cos A +sec A) square =7+tan A square + cot A square

Grade:10

1 Answers

Arun
25763 Points
4 years ago
when we square, we get
sin^2 A + cosec^2 A + 2*sin A* cosecA + cos^2 A + sec^2 A + 2 secA* cosA
as we know we can write,
cosec^2 A = 1 + cot^2 A   &  sec^2 A = 1+ tan^2 A   & sin^2 A+ cos^2 A = 1
& sin A* cosec A = 1 = sec A* cos A
 
hence
1+1+ cot^2 A + 2 + 1+ tan^2 A + 2
7 + tan^2 A + cot^2 A
hence proved

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