If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,` then value of `cos^2theta-sintheta` is equal to 0 (b) `-1` (c) `1` (d) none of thes

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If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,` then value of `cos^2theta-sintheta` is equal to 0 (b) `-1` (c) `1` (d) none of thes

If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,` then value of `cos^2theta-sintheta` is equal to 0 (b) `-1` (c) `1` (d) none of these

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
From the given equation `sin^(2) theta - 2 sin theta + 3 = 5^("sec"^(2)y) + 1`, we get
`(sin theta -1)^(2) + 2 = 5^("sec^(2)y) + 1`
`L.H.S. le 6, R.H.S. ge 6`
Possible solution is `sin theta = -1` when L.H.S. = R.HgtS.
`rArr cos^(2) theta = 0`
`rArr cos^(2) theta - sin theta = 1`

4 views Answered 2023-02-05 15:29