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Question
Match each item given under column C1 to its correct answer given under column C2.
| C1 | C2 |
| (a) `(1 - cosx)/sinx` | (i) `cot^2 x/2` |
| (b) `(1 + cosx)/(1 - cosx)` | (ii) `cot x/2` |
| (c) `(1 + cosx)/sinx` | (iii) `|cos x + sin x|` |
| (d) `sqrt(1 + sin 2x)` | (iv) `tan x/2` |
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Solution
| C1 | C2 |
| (a) `(1 - cosx)/sinx` | (i) `tan x/2` |
| (b) `(1 + cosx)/(1 - cosx)` | (ii) `cot^2 x/2` |
| (c) `(1 + cosx)/sinx` | (iii) `cot x/2` |
| (d) `sqrt(1 + sin 2x)` | (iv) `|cos x + sin x|` |
Explanation:
(a) `(1 - cos x)/sinx = (2sin^2 x/2)/(2sin x/2 cos x/2) = tan x/2`
Hence (a) matches with (iv) denoted by (a) ↔ (iv)
(b) `(1 + cosx)/(1 - cosx) = (2sin^2 x/2)/(2sin^2 x/2) = cot^2 x/2`
Hence (b) matches with (i) i.e., (b) ↔ (i)
(c) `(1 + cosx)/sinx = (2cos^2 x/2)/(2sin x/2 cos x/2) = cot x/2`
Hence (c) matches with (ii) i.e., (c) ↔ (ii)
(d) `sqrt(1 + sin2x) = sqrt(sin^2x + cos^2x + 2sinx cos x)`
= `sqrt((sinx + cosx)^2`
= |(sin x + cos x)|
Hence (d) matches with (iii), i.e., (d) ↔ (iii)
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