Question

prove that (sinA+cosecA)^2+(cosA+secA)^2=7+tan^2A+cot^2A

Answer 1

sin^2A + cosec^2A + 2 sinA × cosecA + cos^2A + sec^2A + 2 sevA × cosA
sin^2 A + cos^A +1 + cot^2 A + 1+ tan^2A + 2 +2
7+ tan^2A + cot^2A

Answer 2

Given:

( sin A+cosec A )² + ( cos A + sec A )²

[ ( a + b )² = a² + b² + 2 a b ]

==> sin²A + cosec²A+2 sin A cosec A + cos²A + sec²A + 2 cos A sec A

[ cosec A = 1 /sin A

sec A = 1 / cos A ]

==> sin²A + cos²A + cosec²A + sec²A + 2 sin A×1/sin A + 2 cos A×1/cos A

[ sin²A+cos²A=1 ]

==> 1 + cosec²A + sec²A+2+2

[1 + tan²A = sec²A

1 + cot²A = cosec²A ]

==> 5 + ( 1 + cot²A ) + ( 1 + tan²A)

==> 5 + 1 + 1 + cot²A + tan²A

==> 7 + tan²A+cot²A

L.H.S = R.H.S [ Proved ]

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