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Question : 22 of 160
Marks:
+1,
-0
Solution:
tan‌15∘=tan(45∘−30∘) =‌=‌ Given,
tan‌30∘ and
tan‌15∘ are the roots of the equation
x2+ax+b=0 ‌∵‌ Sum of roots ‌=tan‌30∘+tan‌15∘=−a ‌⇒‌+‌=−a ‌⇒‌| √3+1+3−√3 |
| √3(√3+1) |
=−a⇒a=‌ Now, product of roots
=tan‌30∘⋅tan‌15∘=b ⇒‌‌b=‌×‌‌. ‌ Now, we have to find
1+a−b.
‌‌ Then, ‌1+a−b=1−‌−‌ ‌=‌| √3(√3+1)−4−√3+1 |
| √3(√3+1) |
=‌| 3+√3−3−√3 |
| √3(√3+1) |
=0
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