Grade 11IIT JEE Entrance Exam

The least value of(further question is present in image)
A 3
B 5
C 9
D 2

Question image for The least value of(further question is present in

Sudhanva G V

7 Years agoGrade 11

1 Answer

Devang

7 Years ago

(secA + cosA)² + (cosecA + sinA)² = sec²A + 2*secA*cosA + cos²A +

cosec²A +2*cosecA*sinA + sin²A

= sec²A + cosec²A +2 +2 +1 ( secA*cosA = 1

cosecA*sinA = 1

sin²A + cos²A = 1 )

= 1/cos²A + 1/sin²A +5

= sin²A + cos²A /sin²A * cos²A +5

= 1/ sin²A * cos²A + 5

= 4/4sin²A * cos²A +5

(secA + cosA)² + (cosecA + sinA)²= 4/sin²2A +5 ….......(1)

we have,

-1 $\leqslant$ sin 2A $\leqslant$ 1

0 $\leqslant$ sin²2A $\leqslant$ 1 (do squre on both side)

$\infty$ $\geqslant$ 1/ sin²2A $\geqslant$ 1

$\infty$ $\geqslant$ 4/sin²2A $\geqslant$ 4 (multiply bu 4)

$\infty$ $\geqslant$ 4/sin²2A +5 $\geqslant$ 9 (add 5) …....(2)

on eq. (1) & (2)

least value of (secA + cosA)² + (cosecA + sinA)² = 9

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The least value of(further question is present in image)A 3B 5C 9D 2

Sudhanva G V

1 Answer

Devang

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The least value of(further question is present in image)
A 3
B 5
C 9
D 2