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Question : 75 of 150
Marks:
+1,
-0
Solution:
The given equation is defined for
x≠‌,‌.
Now,
tan‌x+ secx=2‌cos‌x‌⇒‌+‌=2‌cos‌x‌⇒(sin‌x+1)=2cos2x‌⇒(sin‌x+1)=2(1−sin‌2x)‌⇒(sin‌x+1)=2(1−sin‌x)(1+sin‌x)‌⇒(1+sin‌x)[2(1−sin‌x)−1]=0‌⇒2(1−sin‌x)−1=0‌...[| ∵sin‌x≠−1‌ otherwise ‌cos‌x=0‌ and |
| tan‌x‌ ‌s‌e‌c‌x‌ will be undefined ‌ |
]‌⇒sin‌x=‌‌⇒x=‌,‌‌ in ‌(0,2π)‌
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