Question:
What is the least value of 25 cosec2 x + 36 sec2 x ?
What is the least value of 25 cosec2 x + 36 sec2 x ?
Options:
- 1
- 11
- 121
- 120
- 1
- 11
- 121
- 120
Correct Answer: c)
Explanation:
‘ We ha√e, 25 cosec2x +36 sec? x
i =25(1 + cot? x) + 36(1 + tan? x) i
=25+25c0 x +36 +36 tan’ x
=25+36+25 cot? x +36 tan’ x !
=61+(5 cot x – 6 tan x) +2 X 5x 6>61+60=121.” minimum √alue of (5 cotx – 6 tan 1
2
1 x)” =0 1
! .. Minimum √alue of
2 2
25 cosec” x +36 sec” x = 121
‘ We ha√e, 25 cosec2x +36 sec? x
i =25(1 + cot? x) + 36(1 + tan? x) i
=25+25c0 x +36 +36 tan’ x
=25+36+25 cot? x +36 tan’ x !
=61+(5 cot x – 6 tan x) +2 X 5x 6>61+60=121.” minimum √alue of (5 cotx – 6 tan 1
2
1 x)” =0 1
! .. Minimum √alue of
2 2
25 cosec” x +36 sec” x = 121