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Question : 7 of 61
Marks:
+1,
-0
Solution:
‌| (cosec‌x−cot‌x)(ex−e−x) |
| √3−√2+cos‌x |
Convert,
cosec‌x and
cot‌x into
sin‌x and
ex−e−x=2sin‌hx‌=‌| (⋅2sin‌hx) |
| √3−√2+cos‌x |
‌=‌| 2‌tan‌⋅sin‌hx |
| √3−√2+cos‌x |
×‌| √3+√2+cos‌x |
| √3+√2+cos‌x |
‌=‌| 2‌tan‌⋅sin‌hx(√3+√2+cos‌x) |
| 1−cos‌x |
‌=‌| 2‌tan‌⋅sin‌hx(√3+√2+cos‌x) |
| 1−cos‌x |
‌=‌| ‌⋅sin‌hx(√3+√2+cos‌x) |
| 2sin‌2‌ |
‌=‌| sin‌hx(√3+√2+cos‌x |
| cos‌⋅sin‌‌ |
‌∵x⟶0⇒cos‌⟶1‌ and ‌sin‌‌⟶‌‌sin‌hx⟶x‌=‌=2(√3+√3)=2(2√3)=4√3
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