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The value of (1 + sec 20° + cot 70°) (1 – cosec 20° + tan 70°) is equal to
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- 0
- 1
- 2
- - 1
Correct Option: C
(1 + sec 20° + cot 70°) (1 – cosec 20° + tan 70°)
= (1 + sec 20° + tan 20°) (1 – cosec 20° + cot 20°)
[∵ tan (90° – θ) = cotθ ; cot (90° – θ) = tanθ]
| = |  | 1 + | 1 | + | sin 20° |  | ||
| cos 20° | cos 20° |
| = | | 1 - | 1 | + | cos 20° | | ||
| sin 20° | sin 20° |
| = | . | cos 20° | sin 20° |
| = | sin 20° . cos 20° |
| = | sin 20° . cos 20° |
| = | = 2 | sin 20° . cos 20° |
