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Question : 66 of 150
Marks:
+1,
-0
Solution:
sin‌(θ−α),sin‌θ and
sin‌(θ+α) are in H.P.
‌⇒‌,‌,‌ will be in A.P.
‌∴‌‌‌=‌+‌‌⇒‌=‌| sin‌(θ+α)+sin‌(θ−α) |
| sin‌(θ−α)‌sin‌(θ+α) |
‌⇒‌=‌| 2sin‌θ‌cos‌α |
| sin‌2θ−sin‌2α |
‌⇒sin‌2θ−sin‌2α=sin‌2θ‌cos‌α‌⇒sin‌2θ(1−cos‌α)=sin‌2α‌⇒sin‌2θ(2‌sin‌2‌)=4‌sin‌2‌cos2‌‌⇒1−cos2θ=2cos2‌‌⇒cos2θ=1−2cos2‌ ‌⇒2cos2θ−1=1−4cos2‌‌⇒cos2θ=1−4cos2‌
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