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Question
In the following match each item given under the column C1 to its correct answer given under the column C2:
| Column A | Column B |
| (a) sin(x + y) sin(x – y) | (i) cos2x – sin2y |
| (b) cos (x + y) cos (x – y) | (ii) `(1 - tan theta)/(1 + tan theta)` |
| (c) `cot(pi/4 + theta)` | (iii) `(1 + tan theta)/(1 - tan theta)` |
| (d) `tan(pi/4 + theta)` | (iv) sin2x – sin2y |
Solution
| Column A | Answers |
| (a) sin(x + y) sin(x – y) | (iv) sin2x – sin2y |
| (b) cos (x + y) cos (x – y) | (i) cos2x – sin2y |
| (c) `cot(pi/4 + theta)` | (ii) `(1 - tan theta)/(1 + tan theta)` |
| (d) `tan(pi/4 + theta)` | (iii) `(1 + tan theta)/(1 - tan theta)` |
Explanation:
(a) sin(x + y) sin(x – y) = sin2x – sin2y
(b) cos(x + y) cos(x – y) = cos2x – cos2y
(c) `cot(pi/4 + theta) = (cot pi/4 cot theta - 1)/(cot theta + cot pi/4)`
= `(cot theta - 1)/(cot theta + 1)`
= `(1 - tan theta)/(1 + tan theta)`
(d) `tan(pi/4 + theta) = (tan pi/4 + tan theta)/(1 - tan pi/4 theta)`
= `(1 + tan theta)/(1 - tan theta)`
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