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Question : 22 of 160
Marks:
+1,
-0
Solution:
It is given that,
x=‌ y=‌ The summation of
x and
y is,
x+y‌‌=‌+‌ ‌‌=‌| sin‌θ(1−cos2θ) |
| cos2θ |
+‌| cos‌θ(1−sin2θ) |
| sin2θ |
‌‌=sin‌θ(‌−1)+cos‌θ(‌−1) ‌‌=‌+‌−(sin‌θ+cos‌θ) ‌‌=‌+‌−‌ ‌‌=‌| sin3θ+cos3θ |
| cos2θsin2θ |
−‌ ‌‌=(sin‌θ+cos‌θ)(sin2θ+cos2θ−sin‌θ‌cos‌θ)−‌ ‌‌=‌| ‌(1−sin‌θ‌cos‌θ) |
| (sin‌θ‌cos‌θ)2 |
−‌‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) It is given that
sin‌θ+cos‌θ=‌ Squaring both sides,
sin2θ+cos2θ+2‌sin‌θ‌cos‌θ=‌ 1+2‌sin‌θ‌cos‌θ=‌ sin‌θ‌cos‌θ=‌ Substitute the values in equation (I).
x+y=‌−‌ x+y=‌
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