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Question : 65 of 160
Marks:
+1,
-0
Solution:
‌y=tan2(cos−1√‌)‌‌ Put ‌‌=cos2(2θ)‌‌‌‌‌x2=2cos2(2θ)−1=cos‌4‌‌ Also, ‌0≤‌≤1‌‌‌0≤1+x2≤2‌⇒‌‌x2≤1⇒−1≤x≤1‌⇒‌‌−1≤cos‌4‌θ≤1‌⇒‌‌0≤4θ≤π⇒0≤θ≤‌Differentiating with resped to
x‌⇒‌‌2x‌=−4sin‌4θ‌⇒‌‌‌=‌| −2sin‌4θ |
| √cos‌4‌θ |
‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)and
y=tan2cos−1(cos‌2‌θ)=tan2(2θ)⇒‌‌‌=2‌tan(2θ)× sec2(2θ)×2...‌ (i) ‌⇒‌‌‌‌=‌⇒‌‌‌‌=‌| 4sin‌(2θ)×√cos‌4‌θ |
| cos3(2θ)(−4)sin‌2θ⋅cos‌2‌θ |
‌=−‌‌=‌=‌
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